Peter B Gilkey
202 Deady Hall Mathematics Department
College of Arts and Sciences
University of Oregon
Eugene Oregon 97403 USA
1-541-346-4717 (office phone) 1-541-346-0987 (fax)
email: gilkey@uoregon.edu

Research Articles

  • [1] Curvature and the eigenvalues of the Laplacian for elliptic complexes, Advances in Math, V 10 # 3 (1973), 344-382.
  • [2] Curvature and the eigenvalues of the Dolbeault complex for Kaehler manifolds, Advances in Math, V 11 # 3 (1973), 311-325
  • [3] Local invariants of a Riemannian metric for two dimensional manifolds, Indiana Univ Math J, V 23 # 9 (1974), 855-882.
  • [4] Spectral geometry and the Kaehler condition for complex manifolds, Invent. Math, V 26 (1974), 231-258. A Correction was subsequently posted in V 29 (1975) 81-82 to correct an error found by Prof. T. Tsujishita
  • [5] Spectral geometry of real and complex manifolds, Proc.Symp. in Pure Math, V 27 (1975), 265-280.
  • [6] Spectral geometry and manifolds of constant holomorphic sectional curvature, Proc. Symp. in Pure Math, V 27 (1975), 281-285 (joint work with Jon Sacks).
  • [7] The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary, Advances in Math, V 15 # 3 (1975), 334-360.
  • [8] The spectral geometry of a Riemannian manifold, J.Diff.Geo. V 10 # 4 (1975), 601-618.
  • [9] The index theorem and the heat equation, Publish or Perish Press, Boston Mass (1974), 125pp.
  • [10] Local invariants of an embedded Riemannian manifold, Annals of Math. V 102 (1975), 187-203.
  • [11] Local invariants of a pseudo - Riemannian manifold, Math. Scand. 36 (1975), 109-130.
  • [12] Curvature and the eigenvalues of the Dolbeault complex for Hermitian manifolds, Advances in Math. V 21 # 1 (1976), 61-77.
  • [13] The spectral geometry of symmetric spaces, Trans.AMS V 225 (1977), 341-353.
  • [14] Heat equation, proportionality principle, and the volume of fundamental domains, Differential Geometry and Relativity, ed Cahen and Flato, D.Reidel Publ.Co. 1976, 43-54. (Joint work with R.Cahn and J.Wolf).
  • [15] Local invariants of real and complex Riemannian manifolds, Proc.Symp. in Pure Math. V 30 (1977), 107-110.
  • [16] Smooth invariants of a Riemannian manifold, Advances in Math. V 28 # 1 (1978), 1-10.
  • [17] Lefschetz fixed point formulas and the heat equation, Partial Differential Equations and Geometry (Proc.Park City Conf). Ed C.Byrnes. Marcel Dekker (1979), 91-147.
  • [18] Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian. Compositio Mathematica, V 38 # 2 (1979), 201-240.
  • [19] Topological invariants and absence of an axial anomaly for a Euclidean Taub-NUT metric, Physical Review D, V 17 # 2 (1978), 423-427. (joint with T.Eguchi and A.Hanson).
  • [20] Curvature and the heat equation for the DeRham complex. Geometry and Analysis (Papers dedicated to the memory of V.K.Patodi). Indian Academy of Sciences (1979), 47-80.
  • [21] The residue of the local eta function at the origin, Math.Annalen, V 240 (1979), 183-189.
  • [22] The residue of the global eta function at the origin, Advances in Math., V 40 3 (1981), 290-307.
  • [23] The spectral geometry of the higher order Laplacian, Duke Math.J. V 47 3 (1980), 511-528. (Correction in V 48 4 p 887).
  • [24] Gravitation, gauge theories and differential geometry, Review Section of Physics Letters, North Holland Publishing Company (Amsterdam), V 66 6 (1980), 212-393. (Joint work with T.Eguchi and A.Hanson).
  • [25] The eta invariant for a class of elliptic boundary value problems. Comm on Pure and Appl Math V 36 (1983), 85-131. (joint work with Lance Smith).
  • [26] The twisted index theorem for manifolds with boundary. J.Diff.Geo. 18 (1983), 393-444. (Joint work with Lance Smith)
  • [27] Invariance theory, the heat equation, and the Atiyah-Singer index theorem , Publish or Perish Press, 1985, 349pp. Available on the web: Published on the EMIS server http://www.emis.de/monographs/gilkey/index.html ISBN 0-914098-20-9. See also PDF file provided by Mirko Janc
  • [28] The secondary characteristic classes of locally flat bundles on lens spaces in dimension 3, Differential Geometric Control Theory, ed Brockett, Millman, Sussman (Birkhauser 1983), 237-258.
  • [29] Vector bundles with harmonic curvatures over spheres, Differential Geometry, ed Brooks, Gray, Reinhart (Birkhauser 1983), 89-102.
  • [30] Invariants of the heat equation . Pacific Journal of Mathematics V 117 (1985), 233-254 (joint with H.Fegan).
  • [31] The eta invariant and the K-theory of odd dimensional spherical space forms. Invent.Math. 76 (1984), 421-453.
  • [32] The eta invariant of even dimensional Pinc manifolds, Advances in Math. V 58 3 (1985), 243-284.
  • [33] The eta invariant and secondary characteristic classes of locally flat bundles, Algebraic and Differential Topology- Global Differential Geometry , band 70 (ed G.Rassias), Teubner texte zur Mathematik (Leipzig 1984), 49-87.
  • [34] On sphericalspace forms with meta-cyclic fundamental group which are isospectral but not equivariant cobordant Compositio Mathematica Vol 56 (1985), 171-201.
  • [35] K-theory for spherical space forms (joint work with Max Karoubi), Topology and its applications 25 (1987), 179-184.
  • [36] The eta invariant, Pinc bordism, and equivariant Spinc bordism for cyclic 2-groups (Joint work with A. Bahri), Pacific Journal, V128 (1987), 1-24.
  • [37] Pinc bordism and equivariant Spinc bordism for cyclic 2-groups (Joint with A. Bahri), Proceedings of AMS , Vol 99 (1987), 380-382.
  • [38] The moments of certain complex potentials (joint with H. Fegan), Proceedings of the AMS, Vol 96 (1986), 525-527.
  • [39] The eta invariant and non-singular bilinear products on Rn. Canad. Math. Bull. Vol 30 (2), 1987 p147-154.
  • [40] The eta invariant and real K-theory of lens spaces. Mathematische Zeitschrift, vol 194 (1987), 309-320.
  • [41] Some representations of exceptional Lie algebras, Geometriae Dedicata 25 (1988), 407-416 (with G.Seitz)
  • [42] An analytic computation of the additive structure of $MU*(BZ4)$, "Geometry and Topology", edited by G.M.Rassias, 1989 World Scientific Press, 152-158.
  • [43] The eta invariant and the equivariant unitary bordism of spherical space form groups. Compositio Math 65 (1988), 33-50.
  • [44] Leading terms in the asymptotics of the heat equation, Contemporary Mathematics 73 (1988), 79-85
  • [45] The geometrical index theorem for Clifford modules "Topics in Mathematical Analysis", edited by T.M.Rassias, 1989 World Scientific Press, 315-327.
  • [46] The eta invariant and equivariant Spinc bordism for spherical space form groups. Can. J. Math Vol XL 2 1988, 392-428.
  • [47] The complex bordism of groups with periodic cohomology (with A. Bahri, M. Bendersky, and D. Davis) Trans. AMS V316 (1989), 673-687.
  • [48] K-theory and bordism of spherical space form groups, Simon Stevin 64 (1990), 179-186. (no 2 1990).
  • [49] A Higher order invariant of differential manifolds. Transactions of the American Mathematical Society V 315 1 (1989), 373-388. (Joint with G. Fredricks and P. Parker).
  • [50] The relationship between complex bordism and K-theory for groups with periodic cohomology. Contempory Mathematics, V96 (1989), 19-31. (Joint with A. Bahri and M. Bendersky).
  • [51] Spinors on spherical space forms, Proceedings of the 6th international Colloquium on Differential Geometry (ed Luis A Cordero) Cursos e Congressos da Universidade de Santiago De Compostela 61 (1988), 109-124.
  • [52] Spectral Geometry of Riemannian Manifolds, Contemporary Mathematics V 101 (1989) (Recent Developments in Geometry, Ed. S.Y. Cheng, H. Choi, and Robert E. Greene), 147-154.
  • [53] The eta invariant of even order operators, Differential Geometry (ed F.J.Carreras, O. Medrano, A.M. Naveira), Lecture notes in Mathematics 1410, Springer-Verlag 1989, 202-211.
  • [54] The Geometry of Spherical Space Form Groups, Series in Pure Mathematics Volume 7, World Scientific (1989), 361 pages.
  • [55] Leading Terms in The heat Invariants, joint with T. Branson and B. Orsted, Proceedings of the AMS, 108(2) (1990), 437-450.
  • [56] The Asymptotics of the Laplacian on a manifold with boundary, joint with T. Branson, Comm. in PDE 15(2) (1990), 245-272.
  • [57] Leading terms in the heat invariants for the Laplacians of the DeRham, signature, and spin complexes, joint with T. Branson and B. Orsted, Math. Scand. 66 (1990), 307-319.
  • [58] The higher order differential invariant $\alpha$, Proceedings of the 6th international Colloquium on Differential Geometry (ed Luis A Cordero) Cursos e Congressos da Universidade de Santiago De Compostela 61 (1988), 99-107. (With G. Fredricks and P. Parker)
  • [59] Variational properties of heat equation invariants for operators of Dirac Type. Seminari di Geometria Giornate di Topologia e geometria delle varieta Bologna (1992), 17-38.
  • [60] The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. (With Novica Blazic and Neda Bokan). Proceedings of the Conference on Global Analysis and Global Differential Geometry ed. B. Wegner, Lecture Notes (Springer Verlag) 1481 (1991), 5-17.
  • [61] Heat equation asymptotics of non minimal operators on differential forms J. Math. Phys. V32, 2089-2091 (August, 1991), (With T. Branson and S. Fulling).
  • [62] Functoriality and heat equation asymptotics. Differential geometry and it applications, ed. J. Szenthe and L. Tamasry, V56 Colloquia Mathematica Societatis Janos Bolyai, North Holand (1992), 285-315.
  • [63] Spectral Geometry, in Workshop in the geometry and topology of gauge fields edited by A. Rigas, Mathematica Contemporanea (Brazilian Mathematical Society) V2 (1992), 73-112.
  • [64] On the index of geometrical operators on Riemannian manifolds with boundary. Advances in Mathematics V102 (1993), 129-183.
  • [65] Spectral geometry of the form valued Laplacian for manifolds with boundary. (joint with Bokan and Blazic), Indian J. pure appl. Math 23 (1992), 103-120.
  • [66] An inhomogeneous elliptic complex (with N. Bokan and R. Zivaljevic). Journal D'Analyse Mathematique, V61 (1993), 367-393.
  • [67] Residues of the eta function for an operator of Dirac Type, joint with Tom Branson, Journal of Functional Analysis, V 108 1 (1992), 47-87.
  • [68] Manifolds whose odd higher order curvature operators have constant eigenvalues at the basepoint. Journal of Geometrical Analysis, V 2 2 (1992), 151-156.
  • [69] Residues of the eta function for an operator of Dirac type with local boundary conditions, Joint with T. Branson, Differential Geometry and its applications 2 (1992), 249-267.
  • [70] Asymptotics of Laplacians defined by symmetric connections (joint with N. Bokan) Results in Math V 20 (1991), 589-599.
  • [71] Heat equation asymptotics of the generalized Ahlfors Laplacian on a manifold with boundary. Operator calculus and spectral theory, edited by Demuth, Gramsch, and Schulze, V57 Birkh\"auser (1992), 1-13. (joint with Branson, \O rsted, and Pierzchalski.)
  • [72] Manifolds whose curvature operator has constant eigenvalues at the basepoint. Journal of Geometrical Analysis V 4 (1994), 155-158.
  • [73] Heat equation asymptotics of the form valued Laplacian for manifolds with boundary (with Bokan and Blazic), in Proceedings of the 3rd congress of geometry Thessaloniki 1991, edited by N. K. Stephanidis, Aristotle University of Thessaloniki (1992), 84-95.
  • [74] Heat content asymptotics for operators of Laplace type with Neumann boundary conditions. Joint with S. Desjardins. Math. Z. 215 (251-268 (1994).
  • [75] The functional determinant of a four dimensional boundary value problem. Joint with Tom Branson. TAMS 344 (1994), 479-531.
  • [76] Heat content asymptotics of a Riemannian manifold with boundary. Joint with M. van den Berg. J. Functional Anal V120 (1994), 48-71.
  • [77] Functorality and heat content asymptotics for operators of Laplace type. Joint with van den Berg and Desjardins. Topological methods in nonlinear anlaysis V2 (1993), 147-162. Introduction in GIF format
  • [78] Heat equation asymptotics of elliptic operators with non scalar leading symbol. Joint with Branson, and Pierzchalski. Math. Nachrichten 166 (1994) 207-215. Introduction in GIF format
  • [79] Heat content asymptotics of non minimal operators. Topological methods in non-linear analysis. Vol 3 1994 69-80. Introduction in GIF format
  • [80] Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator. Joint with Swann and Vanhecke. Quart J Math. Oxford 46 (1995), 299-320. Introduction in Gif format
  • [81] Invariants of locally conformally flat manifolds, joint with Tom Branson and Juha Pohjanpelto. Transactions of the AMS 347 (1995) 939-954. Abstract in Gif format
  • [82] Second edition of book Invariance Theory, the heat equation, and the Atiyah-Singer index theorem CRC Press ISBN 0-8493-7874-4 (1994) 516pp. Bibliography by H. Schroeder (Dortmund). This book is out of print. It is available directly from the author at $60 per copy. (Original price $120). Contact gilkey@uoregon.edu
  • [83] The eta invariant and metrics of positive scalar curvature. With B. Botvinnik. Math. Ann. 302 (1995), 507-517. Introduction in Gif format
  • [84] Heat invariants for odd dimensional hemispheres. With with M. van den Berg. Procedings of the Royal Society of Edinburgh 126A (1996), 187-193. Introduction in Gif format
  • [85] Applications of spectral geometry to affine and projective geometry. Joint with N. Bokan and U. Simon. Beitraege zur Algebra und Geometrie vol 35 (1994) 2 p 283-314. Introduction in GIF format
  • [86] The eta invariant, equivariant spin bordism, and metrics of positive scalar curvature. Joint with B. Botvinnik. Operator Theory: Advances and Applications, vol 78 (Birkhauser) p 141-152. Abstract in GIF format
  • [87] When the leading terms in the heat equation asymptotics are coercive. Joint with N. Blazic, N. Bokan, and T. Branson. Houston Math Journal V21 (1995), 75-82. Abstract in GIF format
  • [88] Metrics of positive scalar curvature on spherical space forms. With B. Botvinnik. Canadian Math Journal v48 (1996), 64-80. Introduction in GIF format
  • [89] Second order local affine invariants. Joint with Bokan and Simon. Shirokov volume, Izvestija Vusov Math (Kazan) 5 (396),11-15 (1995) IN RUSSIAN. Abstract in GIF format
  • [90] The eta invariant and the equivariant spin bordism of spherical space form 2 groups. New developments in Differential geometry, ed L. Tamassy and J. Szenthe (1996), v350 Mathematics and its applications, Kluwer Academic Publishers ISBN 0-7923-3822-7, p213-223. with B. Botvinnik. introduction in GIF format
  • [91] Geometry of manifolds and heat content asymptotics for operators of Laplace type. (joint with Bokan and Blazic). Topology of submanifolds VII (ed Dillen, Magid, Simon, Woestijne, Verstraelen). World Scientific (ISBN 981-02-2195-9 1995), p 84-87. Click for further information
  • [92] Eigenvalues of the Laplacian for sphere bundles. Topological methods in non-linear analysis 5 (1995), 341-344. Click for further information
  • [93] Riemannian submersions which preserve the eigenforms of the Laplacian. With J. H. Park. Illinois J Math 40 (1996), 194-201. Click for further information
  • [94] An analytic computation of $ko_{4\nu-1}(BQ_8)$. Joint with Botvinnik. TMNA Vol 6 (1995), 127-135. Click for further information
  • [95] Relating the second and fourth order terms in the asymptotic expansion of the heat equation. Joint with Bokan and Simon. Journal of Geometry, Vol 58 pp 61-65 1997. Click for further information
  • [96] Eigenvalues of the Laplacian and Riemannian submersions. With J. H. Park. Yokohama Math. Journal {\bf 43} (1995), 7-11. Click for further information
  • [97] The functional determinant in the standard conformal class on four dimensional balls and spherical shells.Joint with T. Branson. Proceedings of the 24th National Conference of Geometry and Topology, ed. A. C. Albu and M. Craioveanu, Mirton Publishing Company Timisoara (1996), 59-80. Click for further information
  • [98] The asymptotics of the Laplacian on a manifold with boundary II.Joint with T. Branson and D. Vassilevich. Bollettino dell'Unione Matematica Italiana (7) 11-B (1997) Suppl. fasc. 2 39-67. hep-th/9504029
  • [99] A note on Osserman lorentzian manifolds, Bulletin of the London Math Society vol 29 (1997), no. 2, 227--230. Joint with N. Blazic and N. Bokan. Click for further information
  • [100] The Bochner Laplacian, Riemannian submersions, heat content asymptotics and heat equation asymptotics. Joint with J. H. Park. Czech Math J. 49, 1999, 233-240 Click for further information
  • [101] The Gromov-Lawson-Rosenberg Conjecture: when do manifolds admit metrics of positive scalar curvature. Geometry from the Pacific Rim: Proceedings of the Pacific Rim Geometry Conference held in Singapore Dec. 1994. Publisher: Walter de Gruyter ISBN 3-11-014792-0 (1997) p149-159. Click for further information
  • [102] The spectral geometry of the Hopf fibration, joint with J. V. Leahy and J. H. Park. Journal Physics A {\bf 29} (1996), 5645--5656. Click for further information
  • [103] The local index formula for a Hermitian manifold, joint with S. Nikcevic, and J. Pohjanpelto, Pacific Journal V180 (1997), 51-56. Click for further information
  • [104] A note on the eigenfunctions of the Laplacian for a twisted holomorphic product. Communications of Korean Math. Soc. \#12 (1997) 325-332. Joint with J. H. Park Click for further information
  • [105] The Gromov Lawson Rosenberg conjecture for groups with periodic cohomology. Joint with Botvinnik and Stolz. J. Differential Geometry Vol 46 (1997), 374-405.
  • [106] The Gromov-Lawson-Rosenberg conjecture: the twisted case. Joint with B. Botvinnik. Houston Math J v23 (1997), 143-160.
  • [107] Geometry of differential operators on Weyl manifolds. Joint with Bokan and Simon. Proc R. Soc. London A (1997) vol 453 pages 2527-2536
  • [108] Invariant metrics of positive Ricci curvature on principal bundles, with JeongHyeong Park and Wilderich PAMS Vol 126 1845-1850 (1998)
  • [109] Heat equation with inhomogeneous Dirichlet conditions. Joint with van den Berg. Comm. Analysis and Geometry 7 ( 1999) 279-294.
  • [110] Eigenvalues of the form valued Laplacian for Riemannian submersions. Joint with Leahy and Park. PAMS Vol 126 1845-1850 (1998)
  • [111] A comparison estimate for the heat equation with an application to the heat content of the s-adic von Koch snowflake. Joint with van den Berg. Bull London Math Soc 30 (1998), 404-412
  • [112] Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary, with T. Branson and Dmitri Vassilevich. Journal of Mathematical Physics, Vol 39 (1998) pp. 1040-1049. hep-th/9702178 Erratum-ibid. 41 (2000) 3301
  • [113] Eigenforms of the spin Laplacian and projectable spinors for principal bundles. With Leahy and Park. J. Nucl. Phys. B. 514 [PM] (1998) 740-752.
  • [114] Generalized Osserman Manifolds. Abhandlungen aus dem Mathematischen Seminar der Universit\"at Hamburg, 68 (1998), 125-127
  • [115] Pontrjagin forms, Chern Simons classes, Codazzi transformations, and affine hypersurfaces. Joint with Blazic and Bokan. Journal of Geometry and Physics Vol 27 (1998), 333-349.
  • [116] Logarithmic terms in asymptotic expansions of heat operator traces, with Gerd Grubb. Comm on PDE Vol 23 (1998) p 777-792.
  • [117] Pseudo Riemannian manifolds whose generalized Jacobi operator has constant characteristic polynomial. Joint with Stanilov and Videv. J. Geom 62 (1998) 144--153.
  • [118] The eta invariant and the connective $K$ theory of cyclic 2 groups. Joint with Barrera-Yanez. Annals of Global Analysis and Geometry Vol 17 (1999), 289--299.
  • [119] A remark on the heat equation with inhomogeneous Neumann boundary conditions Joint with M. van den Berg. J. Potential Analysis Vol 14, 269--274 (2001)
  • [120] Spectral invariants of affine hypersurfaces. Joint Bokan and Simon. Publications de l'Institut Mathematique Publications de l'Institut Mathematique Vol 64 (1998), 133-145.
  • [121] Riemannian manifolds whose skew-symmetric curvature operator has constant eigenvalues II. Differential geometry and applications (ed Kolar, Kowalski, Krupka, and Slovak) Publ Massaryk University Brno Czech Republic 1999 ISBN 80-210-2097-0, 73-87.
  • [122] The eta invariant of pin manifolds with cyclic fundamental groups. Periodica Math. Hungarica. Vol 36 (1998) 139-170.
  • [123] The eigenforms of the complex Laplacian for a holomorphic Hermitian submersion, Nagoya Math. J. 156, 1999, 1-23 joint with Leahy and Park.
  • [124] The heat content asymptotics for variable geometries. J. Phys. A: Math. Gen. 32 (1999) 2825-2834.
  • [125] Riemannian manifolds whose skew-symmetric curvature tensor has constant eigenvalues (with J Leahy and H Sadofsky).
  • [126] The heat content asymptotics of a time dependent process. joint with van den Berg.
  • [127] Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture. With JV Leahy and JH Park. ISBN 0-8493-8277-7 Publ 1999 CRC Press 279 pp
  • [128] Heat asymptotics with spectral boundary conditions. Joint with Dowker and Kirsten. Eds: B. Booss-Bavnbek, K. Wojciechowski, Geometric Aspects of Partial Differential Equations. Proceedings of a Minisymposium on Spectral Invariants, Heat Equation Approach, September 18-19, 1998, Roskilde, Denmark. Contemporary Mathematics Vol 242, Amer. Math. Soc., Providence, R.I., 1999. pp 107-124. Archive hep-th/0004020
  • [129] Spinors, Spectral Geometry, and RIemannian Submersions, with J Leahy and JH Park. Published on the EMIS server at: http://cdns.emis.de/monographs/GLP/index.html. (Originally published as Lecture Notes Series \#40, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University 1998, 143 pages. Abstract available from Seoul National University: http://www.garc.snu.ac.kr/print/lecture/40.html)
  • [130] Heat kernel asymptotics with mixed boundary conditions. Branson, Gilkey, Kirsten, and Vassilevich. Nuclear Physics B 563 (1999), 603-626. hep-th/9906144
  • [131] Spinors, self-duality, and IP algebraic curvature tensors of rank 4. Joint with Semmelman. ESI preprint 616.Proceedings of the Symposium in Contemporary Mathematics in honor of 125 years of faculty of Math at Univ Belgrade, N. Bokan Editor ISBN 86-7589-014-1, pp 1--12 (2000)
  • [132] Relating algebraic properties of the curvature tensor to geometry. Novi Sad J Math V29 (1999), 109--119.
  • [133] Heat content asymptotics of time dependent processes with source terms and with inhomogeneous boundary conditions. Joint with JH Park. Mod. Phys. Lett. A. Vol 15 \#18 (2000) pp 1165-1179.
  • [134] Bundles over projective spaces and algebraic curvature tensors. Journal of Geometry 71 (2001), 54--67.
  • [135] Algebraic curvature tensors which are $p$ Osserman. Differential Geometry and its Applications, 14 (2001) 297--311.
  • [136] Geometric consequences of some algebraic properties of the curvature tensor. Bull. Math. Soc. Sc. Math. Roumanie Tome 45 (93) (2000), 255-265. Joint with R. Ivanova
  • [137] Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2. Periodica Mathematica Hungarica, Vol 44 (2002), 7--26. Joint with T. Zhang math.DG/0205080
  • [138] On properties of the asymptotic expansion of heat trace for the N/D problem (with Dowker and Kirsten). hep-th/0010199 INT J MATH 12 (2001), 505-517
  • [139] Heat Trace Asymptotics of a time dependent process", joint with Klaus Kirsten and JeongHyeong Park. J. Phys. A:Math. Gen Vol 34 (2001) 1153-1168. hep-th/0010136
  • [140] Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario. Nuclear Physics B., 601 (2001), 125--148 hep-th/0101105 Joint with Kirsten and Vassilevich.
  • [141] The geometry of the skew-symmetric curvature operator in the complex setting. Joint with R. Ivanova. Global Differential Geometry: The Mathematical Legacy of Alfred Gray Ed. M Fernández and J. Wolf, Contemporary Mathematics vol 288 - ISBN 0-8218-2750-2 (2001), 325-333 http://arXiv.org/PS_cache/math/pdf/0205/0205081.pdf
  • [142] The Jordan normal form of Osserman algebraic curvature tensors, with R. Ivanova. Resul. Math. 40 (2001) 192-204. Paper in DVI format.
  • [143] Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature tensor has constant Jordan normal form. Joint with T. Zhang. Houston Math J 11 (Chern Volume) 28 (2002), 311--328. math.DG/0205079
  • [144] Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor. Available from World Scientific ISBN 981-02-4752-4
  • [145] Curvature tensors whose Jacobi or Szabo operator is nilpotent on null vectors. With I. Stavrov. Bulletin of the London Math Soc 34 (2002), 650--658. math.DG/0205074
  • [146] The Jordan normal form of higher order Osserman algebraic curvature tensors. Joint with R. Ivanova. Comment. Math. Univ. Carolinae 43 (2) (2002) 231-242 Comment. Math. Univ. Carolinae.math.DG/0205073
  • [147] Spacelike Jordan Osserman algebraic curvature tensors in the higher signature setting. Joint with R. Ivanova. Proceedings Valencia Conference. World Scientific. ISBN 981-02-4906 (2002) 179-186, math.DG/0205072
  • [148] Heat content asymptotics for oblique boundary conditions. Joint with K. Kirsten and JH Park. Letters in Mathematical Physics 59 (2002) 269-276. http://www.mis.mpg.de/preprints/2002/prepr2002\_48.html
  • [149] Heat asymptotics with spectral boundary conditions II. With Kirsten. Proceedings of the Royal Society of Edinburgh A 133 (2003) 333--361 math-ph/0007015
  • [150] Higher order Jordan Osserman, Pseudo-Riemannian manifolds, joint with Ivanova and Zhang, Class and Quantum Gravity, 19 (2002), 4543-4551. math.DG/0205269
  • [151] Heat content asymptotics for spectral boundary conditions, joint with Kirsten and Park, Trends in Mathematics (Kaist) 5 (2002), 49--58. math-ph/0209012
  • [152] Szabo Osserman IP Pseudo-Riemannian manifolds. Joint with Ivanova and Zhang. Publicationes Mathematicae Publ. Math. Debrecen 62 (2003), 387--401. math.DG/0205085
  • [153] The eta invariant and the real connective $K$-theory of the classifying space for quaternion groups, joint with Barrera-Yanez, Annals Global Analysis, vol 23 (2003), 173--188 math.DG/0205084
  •  [154] Duality symmetry of the p-form effective action and super trace of the twisted de Rham complex, with K. Kirsten, D. Vassilevich, and A. Zelnikov, Nuclear Physics B. Nuclear Physics B 648 (2003), 542--556. hep-th/0209125
  • [155] Heat trace asymptotics defined by transfer boundary conditions, Joint with Kirsten and Vassilevich. Letters in Mathematical Physics vol 63 (2003), 29--37. hep-th/0208130
  • [156] Heat content asymptotics with transmittal and transmission boundary conditions. Joint with Kirsten. J. London Math Soc. (2) 68 (2003), 431--443 math-ph/0206022
  • [157] Nilpotent Szabo, Osserman and Ivanov-Petrova pseudo-Riemannian manifolds, joint with B. Fiedler. Contemporary Mathematics 337 (Recent Advances in Riemannian and Lorentzian Geometries), 2003, pp 53-64. math.DG/0211080.
  • [158] Supertrace divergence terms for the Witten Laplacian, with joint with Kirsten and Vassilevich. Potential Analysis 20 (2004) 223-235. math-ph/0212023
  • [159] Jordan Szabo algebraic covariant derivative curvature tensors, joint with Raina Ivanova and Iva Stavrov. Contemporary Mathematics 337 (Recent Advances in Riemannian and Lorentzian Geometries), 2003, pp 65--76. math.DG/0211089.
  • [160] Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary, joint with Kirsten and Vassilevich. Journal of Geometry and Physics, Volume 49, Issues 3-4, March 2004, Pages 249--271. math-ph/0211020
  • [161] Strong ellipticity and spectral properties of chiral bag boundary conditions. Joint with C.G. Beneventano, K. Kirsten, and E.M. Santangelo. J. Phys. A 2 36 No 45 (14 November 2003) 11533--11543 hep-th/0306156
  • [162] Asymptotic Formulae Spectral Geometry, to be published by CRC Press 26 Dec 2003
  • [163] Heat content, torsional rigidity and generalized Hardy inequalities for complete Riemannian manifolds, with M. van den Berg. Bulletin of the London Mathematical Society 36 (2004), 577--586math.DG/0302255
  • [164] Manifolds which are Ivanov-Petrova or k-Stanilov. Joint with S. Nikcevic and V. Videv. Journal of Geometry. Volume 80 (2004), 82--94. math.DG/0310118
  • [165] Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds, with S. Nikcevic. Class. Quantum Grav 21 (2004), 497--507. math.DG/0310024
  • [166] Nilpotent Spacelike Jorden Osserman pseudo-Riemannian manifolds, joint with S. Nikcevic. ``Proceedings of the Winter School `Geometry and Physics', Srni (2003)''. Rendiconti del circolo mathematico di Palermo Serie II Suppl. 72 (2004) 99--105. math.DG/0302044
  • [167] Conformally Osserman manifolds and conformally complex space forms, joint with N. Blazic, International Journal of Geometric Methods in Modern Physics (2004), 97--106; math.DG/0311263
  • [168] Curvature homogeneous pseudo-Riemannian manifolds which are not locally homogeneous. Joint with C. Dunn. Complex, contact and symmetric

    • manifolds, 145--152, Progr. Math., 234, Birkhauser Boston, Boston, MA, 2005. math.DG/0306072.
  • [169] Heat content asymptotics for operators of Laplace type with spectral boundary conditions with K. Kirsten, and JH. Park. Letters in Mathematical Physics 68 (2) (2004) 67--76 math-ph/0308021
  • [170] The structure of algebraic covariant derivative curvature tensors, joint with J. Diaz-Ramos, B. Fiedler, and E. Garcia-Rio; Int. J. Geom. Methods Mod. Phys. 1 (2004), no. 6, 711--720 math.DG/0404060
  • [171] Complete curvature homogeneous pseudo-Riemannian manifolds, joint with S. Nikcevic. Classical and Quantum Gravity, volume 21, issue 15, pages 3755 - 3770. math.DG/0402282
  • [172] Eigenforms of the Laplacian for Riemannian V-submersions. Tohoku Math J 57 (2005), 505--519. Joint with J. H. Park. math.DG/0310439
  • [173] Curvature homogeneous signature $(2,2)$ manifolds. "Differential Geometry and its Aplications, Proc. Conf. Prague, August 30-September 3, 2004 Charles University, Prague (Czech Republic), editors Bures, Kowalski, Krupka, Slovak, MATFYZPRESS (2005), ISBN 80-86732-63-0, 29--44. Web download See also math.DG/0408316
  • [174] Complete $k$-curvature homogeneous pseudo-Riemannian manifolds, with S. Nikcevic. Annals of Global Analysis and Geometry. Vol 27 (2005), 87--100. math.DG/0405024. There was a difficulty viewing this paper electronically on Springer - it has been fixed. Here is a PDF file .
  • [175] Conformally Osserman manifolds and self-duality in Riemannian geometry. Joint with N. Blazic. "Differential Geometry and its Aplications, Proc. Conf. Prague, August 30-September 3, 2004 Charles University, Prague (Czech Republic), editors Bures, Kowalski, Krupka, Slovak, MATFYZPRESS (2005), ISBN 80-86732-63-0, 15--18. Web download see also math.DG/0504498
  • [176] Complete $k$-curvature homogeneous pseudo-Riemannian manifolds $0$-modeled on an indecomposible symmetric space, joint with S. Nikcevic. Topics in Almost Hermitian Geometry and the Related Fields, World Scientific (2005), 87--104. math.DG/0504050
  • [177] Heat kernel coefficients for chiral bag boundary conditions, joint with K. Kirsten and G. Esposito. J. Phys. A: Math. Gen. 38 No 10 (11 March 2005) 2259--2276. math.AP/0510156
  • [178] Generalized plane wave manifolds, Kragujevac J. Math. {\bf 28} (2005), 113--138, joint with S. Nikcevic. math.DG/0505253
  • [179] The spectral geometry of the Weyl conformal tensor. Joint with N. Blaic, S. Nik\cevic, and U. Simon. Banach Center Publ. 69 (2005), 195-203 math.DG/0310226
  • [180] Affine curvature homogeneous 3-dimensional Lorentz Manifolds. Joint with S. Nikcevic. International Journal of Geometric Methods in Modern Physics Vol. 2, No. 5 (2005) 737-749; math.DG/0504163
  • [181] Eta invariant with spectral boundary conditions, joint with K. Kirsten and J.H. Park. J. Phys. A: Math. Gen. 38 8103-8122 (2005); math-ph/0406028
  • [182] Isometry groups of $k$-curvature homogeneous pseudo-Riemannian manifolds, joint S. Nikcevic, Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 79 (2006), 99--110. math.DG/0505598
  • [183] Heat Content Asymptotics for Riemannian manifolds with Zaremba boundary conditions, with M. van den Berg, K. Kirsten, and V. A. Kozlov, Potential Analysis 26 (2007), 225-254; see also math-ph/0506076
  • [184] Stability theorems for chiral bag boundary conditions. With K. Kirsten. math.AP/0510152 Letters in mathematical physics V73 147 - 163 (2005).
  • [185] Jacobi--Tsankov manifolds which are not $2$-step nilpotent, Proceedings of the conference Contemporary Geometry and Related Topics (2007), 63--80. ISBN 86-7589-059-1, joint with M. Brozos-Vazquez and S. Nikcevic. math.DG/0609565
  • [186] Pseudo-Riemannian manifolds with Commuting Jacobi Operators, with M. Brozos-Vazquez. Rendiconti Del Circolo Matematico di Polermo Vol 55 (2006), 163--174. math.DG/0608707
  • [187] Manifolds with commuting Jacobi operators, joint with M. Brozos-Vazquez. Journal Geometry Volume 86 (2006), 21--30; math.DG/0507554
  • [188] The global geometry of Riemannian manifolds with commuting curvature operators, joint with M. Brozos-Vazquez. Journal Fixed Point Theory (2007), 87--96; Max Planck Institute Preprint 2006-88.
  • [189] Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold. Joint with Brozos-Vazquez and Garcia-Rio. Advances in Geometry. Volume 8, Issue 3, Pages 353Ð365. See alsoMPI preprint #135-2006
  • 190] Algebraic theory of affine curvature tensors, joint with N. Blazic, S. Nikcevic, and U. Simon. Archivum Mathematicum, Masaryk University (Brno, Czech Republic) ISSN 0044-8753, tomus 42 (2006), supplement: Proceedings of the 26th Winter SchoolGeometry and Physics 2006 (SRNI), 147--168. math.DG/0609759
  • [191] Complex Osserman Algebraic Curvature Tensors and Clifford Families, joint with M. Brozos-Vazquez. Houston Journal  of Mathematics, Vol 34 (2008), 677--702. math.DG/0608749.
  • [192] Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds. "Proceedings of the XV International Workshop on Geometry and Physics" (Puerto de la Cruz, Tenerife, Canary Islands, Spain September 11-16 2006). Publ. de la RSME {\bf 10} (2007), 57--66. Joint with M. Brozos-Vazquez, E. Garcia-Rio, and R. Vazquez-Lorenzo. math.DG/0611279 and MPI preprint.
  • [193] Projectively Osserman manifolds. Joint with Brozos-Vazquez, S. Nikcevic, and U. Simon. Publicationes Mathematicae Debrecen72 (2008), 359--370; http://arxiv.org/abs/0708.1210.
  • [194] The spectral geometry of the canonical Riemannian submersion of a compact Lie Group, J. Geometry and Physics 57 (2007), 2065-2076. Joint with Dunn and Park. MPI preprint
  • [195] The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds. Joint with Brozos-Vazquez, Imperial College Press ISBN 978-1-86094-785-8 see also (978-1-86094-785-8)
  • [196] Pseudo-Riemannian Jacobi--Videv Manifolds. Joint with Stana Nikcevic, IJGMMP 4 (2007), 727--738. http://arxiv.org/abs/arXiv:0708.1096
  • [197] Expected volume of intersection of Wiener sausages and heat kernel norms on compact Riemannian manifolds with boundary. Joint with van den Berg. Potential Analysis 27 (2007), 301-312. http://arxiv.org/abs/math/0609603
  • [198] Examples of signature $(2,2)$ manifolds with commuting curvature operators, J. Phys. A: Math. Theor. 40 (2007) 13149-13159. Joint with M. Brozos-Vazquez, E. Garc{\i}a--R{\i}o, and R. Vazquez-Lorenzo. MPI Preprint 73/2007: http://www.mis.mpg.de/preprints/2007/preprint2007\_73.pdf
  • [199] The classification of simple Jacobi--Ricci commuting algebraic curvature tensors, joint with S. Nikcevic, Note di Matematica, supplemento n.1 to vol. 28, 2008 (University of Lecce) 341-348. arXiv:0710.2080
  • [200] Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series, joint with C. Dunn and J-H. Park. MPI preprint: http://www.mis.mpg.de/preprints/2007/prepr2007\_72.html. J. Phys. A: Math. Theor. 41 No 13 (4 April 2008) 135204.
  • [201] Heat Content, Heat Trace, and Isospectrality, Accepted by the Proceedings of the sixth workshop on Lie Theory and Geometry (ed. C. Gordon, J. Tirao, J. Vargas, and J. Wolf). %Accepted 15 Sept 2008. Contemporary Math 491 (2009), 115--124. http://arxiv.org/abs/0802.2948.
  • [202] Heat Content Asymptotics with singular initial temperature distributions. Joint with M. van den Berg and R. Seeley. J. Funct. Anal. 254 (2008), 3093-3122. http://arxiv.org/abs/arXiv:0803.0675
  • [203] Geometrical representations of equiaffine curvature operators, joint with S. Nikcevic, Results in Mathematics 52 (2008), 281--287 math.DG/0802.0265
  • [204] Curvature structure of Self-dual 4-manifolds, joint with N. Blazic, S. Nikcevic, I. Stavrov. IJGMMP vol 5 issue 7, 1191-1204. http://arxiv.org/abs/0808.2799.
  • [205] Geometric realizations of generalized algebraic curvature operators. Joint with S. Nikcevic and D. Westerman. J. Math. Phys. 50, 013515 (2009). http://arxiv.org/abs/0811.3180
  • [206] Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators. Joint with S. Nikcevic and D. Westerman. Conference Proceedings of the VIII International Colloquium on Differential Geometry (World Sci. Publ. Co.) (2009) 175--184 ISBN 10 981-4261-16-5 http://arxiv.org/abs/0811.3841
  • [207] Videv models and manifolds, joint with V. Videv. J. Geom. 92 (2009), 60--68. arxiv.org/abs/math.DG/0605464.
  • [208] The geometry of modified Riemannian extensions. E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey, and R. Vazquez-Lorenzo. Proc. R. Soc. A. (2009) 465, 2023-2040. doi:10.1098/rspa.2009.0046 arxiv.org/abs/arXiv:0901.1633
  • [209] Geometric realizations of curvature models by manifolds with constant scalar curvature. By M. Brozos-Vazquez, P. Gilkey, H. Kang, S. Nikcevic, G. Weingart. Differential Geometry and its Applications 27 (2009), 696--701. doi:10.1016/j.difgeo.2009.05.002 http://arxiv.org/abs/arXiv:0811.1651.
  • [210] Heat trace asymptotics with singular weight functions, joint with M. van den Berg, P. Gilkey, and R. Seeley, http://arxiv.org/abs/0806.1706. Communications in Analysis and Geometry, Vol 17 (2009), 529--563
  • [211] Geometric Realizations of para-Hermitian curvature models, accepted Results in Mathematics 10 November 2009, M. Brozos-Vazquez, P. Gilkey, S. Nikcevic, and R. V{a}zquez-Lorenzo. http://arxiv.org/abs/arXiv:0902.1697.
  • [212] The Geometry of Walker Manifolds Miguel Brozos-Vazquez, Eduardo Garcia-Rio, Peter Gilkey, Stana Nikcevic, Ramon Vazquez-Lorenzo Synthesis Lectures on Mathematics and Statistics, Vol. 2, No. 1, Morgan and Claypool, Pages 1-179 (2009). ISBN 9781598298192
  • [213] Geometric Realizations of Hermitian curvature models joint with M. Brozos-Vazquez, H. Kang, and S. Nikcevic. arxiv.org/abs/arXiv:0812.2743
  • [213] Geometric Realizations of Hermitian curvature models joint with M. Brozos-Vazquez, H. Kang, and S. Nikcevic. arXiv:0812.2743 To appear J. Math Soc. Japan.
  • [214] Geometric theory of equiaffine curvature tensors, joint with S. Nikcevic, and U. Simon. To appear Results in Math. arxiv.org/abs/0903.5269
  • [215] Four-dimensional Osserman metrics of neutral signature. Joint with E. Garc\'{\i}a--R\'{\i}o, and M. E. Vazquez-Abal, R. Vazquez-Lorenzo. http://arxiv.org/abs/0804.0436v1 Accepted 25 Sep 2009 by Pacific J. M.
  • [216] The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order, joint with R.J. Miatello, R.A. Podesta. http://arxiv.org/abs/0910.0635 Accepted AGAG 19 October 2009.
  • [217] Geometric realizations of Kaehler and of para-Kaehler curvature models, joint with M. Brozos-V\'azquez and E. Merino, to appear IJGMMP v7, N3 (May 2010). arXiv:0909.3473.

    Submitted and in preparation



  • Web page updated 10 November 2009 by Peter B Gilkey 202 Deady Hall, Department of Mathematics at the University of Oregon, Eugene OR 97403-1222, U.S.A. Phone 1-541-346-4717 Email:peter.gilkey.cc.67@aya.yale.edu of Deady Spider Enterprises