Expository Papers of
Peter B. Gilkey ,
.
[E0] The index theorem, Lecture notes for course at I. C. T. P. (Trieste)
1988.
[E1] Hearing the shape of a drum, Current Contents, V30 32 (1990), p 16.
[E2] The index theorem and Clifford modules, Forty more years of ramifications:
Spectral asymptotics and its applications, ed. S. A. Fulling and F.
J. Narcowich (vol I Discourses in Mathematics and its Applications, publ
Texas A\&M) (1991), 265-316.
[E3] Heat Equation Asymptotics. Proc. Symp. Pure and Applied Math. V54
(1993), 317-336.
[E4] Asymptotic expansions in spectral geometry. Geometry in partial
differential equations ed. A. Prastary and T. Rassias. World Scientific
(1994), p 100-113. Expository.
[E5] Heat content asymptotics of Riemannian manifolds, joint with M. Van
den Berg and S. Desjardins. Differential Geometry and its Applications
ed. O. Kowalski and D. Krupka (proceedings of 5th international conference
1992 on differential geometry and its applications at Silesian University),
Silesian University at Opava (1993) ISBN 80-901581-0-2, p61-64.Differential
Geometry and Its Applications, Proc. Conf. 1992, Opava (Silesian University,
Opava, 1993). (electronic edition: ELibEMS, http://www.emis.de/proceedings/)
[E6] Applications of spectral geometry to geometry and topology. Lecture
notes series 12. Research institute of mathematics global analysis research
center. Seoul National University, Seoul 151-742 Korea (1993), 78pp.
[E7] Heat content asymptotics of elliptic operators with non scalar leading
symbol, in "Proceedings of workshops in pure mathematics, Volume 13, Part
III: Differential Geometry and Related Topics" published by "Pure Mathematics
Research Association, The Korean Academic Council" (1993), 127-152.
[E8] The Gromov Lawson Rosenberg conjecture: when do manifolds admit metrics
of positive scalar curvature. Heat kernel techniques and quantum gravity,
edited by S. A. Fulling, Discourses in mathematics and its applications
4. 449-460. ISBN 0-9630728-3-8
[E9] Heat equation and heat content asymptotics. Heat kernel techniques
and quantum gravity, edited by S. A. Fulling, Discourses in mathematics
and its applications 4. 1-10. ISBN 0-9630728-3-8 [E10] Asymptotic spectra
for Weyl geometries. Romanian conference on geometry. Joint with Bokan
and Simon. To appear ANALELE STIINTIFICE ALE UNIVERSITATII "AL.I.CUZA"
DIN IASI, Tomul XLII,Supliment,s.I.a Matematica, 1996, p (59-71?)
[E12] Spectral geometry of Riemannian submersions. Joint with Leahy and
Park. Zbornik radova, Mathematical institute of SANU, Belgrade, Yugoslavia
1997 New Series Book 6 p 36-54. Mathematical institute of SANU, Belgrade,
Yugoslavia
[E13] Pseudo-Riemannian Osserman manifolds. With Blazic, Bokan, and Rakic.
Journal of Balkan Society of Geometers, editors Udriste and Miron. vol.
2, no 2, 1997
[E14] The Atiyah-Singer index theorem. Handbook of Differential Geometry}
vol 1 (Elsevier), edited by Franki Dillen (2000) 709--746
[E15] Heat Content Asymptotics. 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 125-134
[E16] Articles for Encyclopedia of Mathematics (Kluwer academic publishers):
Heat content asymptotics, Osserman conjecture, Gromov-Lawson conjecture,
and Ivanov-Petrova metrics. See Encyclopedia
of Mathematics, Supplement II Michiel Hazewinkel Ed ISBN 0-7923-6114-8,
2000. 620pp, Kluwer Academic Publisher
[E17] Curvature, Spectra, and Riemannian Submersions, acecepted for publication
in Trends in Mathematics Information Center for Mathematical Sciences KIAST
(Korea) Volume 2, December 1999 pp164--169/ Joint with JH Park
[E18] Riemannian submersions and heat content asymptotics. Proceedings
of the first workshop for women mathematicians. Volume 1 (1999) ed Suk
Young Lee (Institute of Mathematical Sciences, EWHA WOMANS UNIVERSITY)
pp23--30. Joint with JH Park
[E19] Geometric properties of the curvature operator. Proceedings
of Beijing Conference ("Geometry and Topology of Submanifolds, vol. X",
World Scientific, Singapore eds: W.H. Chen, A.-M. Li, U. Simon, L. Verstraelen,
C.P. Wang, and M. Wiehe) ISBN 981-02-4476-2 p 62-70 (2000)
[E20] Asymptotics of the heat equation with `exotic' boundary conditions
or with time dependent coefficients. Nucl. Phys. B. (Proc. Suppl) 104 (2002)
63--70. Joint with Kirsten, Park, Vassilevich. http://arXiv.org/abs/math-ph/0105009
[E21] Heat Content Asymptotics, Joint with J. H. Park , Nucl. Phys.
B. (Proc. Suppl) 104 (2002) 185--188
[E22] Complex IP pseudo-Riemannian algebraic curvature tensors.Joint with
R. Ivanova PDES, Submanifolds and affine differential geometry, Banach
center publications, vol 57, Institute of mathematics, Polish academy of
sciences, Warszawa 2002, 195--202. http://arXiv.org/abs/math.DG/0205078
[E23] The spectral geometry of the Riemann curvature tensor, joint with
Ivanova and Zhang. Trends in Mathematics, 5 (2002), 105--114 http://arXiv.org/abs/math.DG/0206129
[E24] The spectral geometry of the Riemann curvature operator in the higher
signature setting. Joint with C. Dunn, R. Ivanova, and S. Nikcevic. To
appear NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS, special volume
dedicated to Professor Grigorios Tsagas, scheduled to appear in September,2004.
math.DG/0312249
[E25] The Index Theorem, joint with
I. Ivanova, K. Kirsten, and JH Park, Encyclopedia
of Mathematical Physics (Elsevier Academic) eds. J.-P. Francoise, G.L.
Naber and Tsou S.T. Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3),
volume 3 page 23--31.
[E26] Characteristic Classes. Joint with
R.Ivanova and S. Nikcevic. Encyclopedia
of Mathematical Physics (Elsevier Academic) eds. J.-P. Francoise, G.L.
Naber and Tsou S.T. Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3),
volume 1 page 488-495.
[E27] The spectral geometry of operators
of Dirac and Laplace type.
Handbook of Global Analysis"
(Demeter Krupka and David Saudners), p287-324.
[E28] Stanilov--Tsankov--Videv Theory, SIGMA 3 (2007), 095, 13 pages;
arXiv:0708.0957, joint with M. Brozos-V\'azquez, B. Fiedler, E.
Garc\'{\i}a--R\'{\i}o, S. Nik\v cevi\'c,
G. Stanilov, Y. Tsankov, R. V\'azquez-Lorenzo, and V. Videv;
http://arxiv.org/abs/0708.0957. Published as
http://www.emis.de/journals/SIGMA/2007/095/sigma07-095.pdf
[E29] Geometric realizations of curvature,
M. Brozos-V{\'a}zquez, P. Gilkey, and S. Nik\v cevi\'c
Nihonkai Mathematical Journal Issue 1 Volume 20 (2009) 1--24;
arXiv:0904.1192
[E30] Puffini-Videv models and manifolds,
E. Puffini and V. Videv. https://arxiv.org/abs/math/0605464