Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T13:49:35.262Z Has data issue: false hasContentIssue false
  • English
  • Français

Metrics of Positive Scalar Curvature on Spherical Space Forms

Published online by Cambridge University Press:  20 November 2018

Boris Botvinnik  and
Peter B. Gilkey
Boris Botvinnik
Affiliation:
Mathematics Department University of Oregon Eugene, Oregon 97403 U.S.A., e-mail: gilkey@math.uoregon.edu
Peter B. Gilkey
Affiliation:
Mathematics Department University of Oregon Eugene, Oregon 97403 U.S.A., e-mail: botvinnik@math.uoregon.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We use the eta invariant to show every non-simply connected spherical space form of dimension m ≥ 5 has a countable family of non bordant metrics of positive scalar curvature.

Keywords

58G1258G2553A5053C2555N22

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 64 - 80
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Atiyah, M.F., Patodi, V.K., and Singer, I.M., Spectral asymmetry and Riemannian geometry, Bull. London Math. Soc. 5(1973), 229–234. Spectral asymmetry and Riemannian geometry I, II, III, Math. Proc. Cambridge Philos. Soc. 77(1975), 43–69. 78(1975), 405–432. 79(1976), 71–99.Google Scholar
2. Botvinnik, B. and Gilkey, P., The eta invariant and metrics of positive scalar curvature, Math. Anal., 302(1995), 507–517.Google Scholar
3. Botvinnik, B., Gilkey, P., and Stolz, S., The Gromov-Lawson-Rosenberg conjecture for groups periodic cohomology, Inst. Hautes Etudes Sci. Publ. Math. 62(1994), preprint.Google Scholar
4. Donnelly, H., Eta invariants for G spaces, Indiana Univ. Math. J. 27(1978), 889–918.Google Scholar
5. Gajer, P., Riemannian metrics of positive scalar curvature on compact manifolds with boundary, Ann. Global Anal. Geom. 5(1987), 179–191.Google Scholar
6. Giambalvo, V., pin and pin7 cobordism, Proc. Amer. Math. Soc. 39(1973), 395–401.Google Scholar
7. Gilkey, P., The Geometry of Spherical Space Form Groups, Series in Pure Math. 7, World Scientific Press, 1989.Google Scholar
8. Gilkey, P., Invariance Theory, the heat equation, and the Atiyah-Singer index theorem, 2 n d Ed, CRC press, 1995.Google Scholar
9. Gilkey, P., The eta invariant for even dimensional pinc manifolds, Adv. in Math. 58(1985), 243—284.Google Scholar
10. Gromov, M. and Lawson, H.B., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111(1980), 423–434. see also Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Etudes Sci. Publ. Math. 58(1983), 83—196.Google Scholar
11. Hitchin, N., Harmonic spinors, Adv. in Math. 14(1974), 1—55.Google Scholar
12. Kreck, M. and Stolz, S., Nonconnected moduli spaces of positive sectional curvature metric, J. Amer. Math. Soc. 6(1993), 825–850.Google Scholar
13. Lichnerowicz, A., Spineurs harmoniques, C. R. Acad. Sci. Paris 257(1963), 7–9.Google Scholar
14. Miyazaki, T., On the existence of positive curvature metrics on non simply connected manifolds, J. Fac. Sci. Univ. Tokyo Sect IA Math. 30(1984), 549–561.Google Scholar
15. Rosenberg, J., C* algebras, positive scalar curvature, and the Novikov conjecture, II. In: Geometric Methods in Operator Algebras, Pitman Res. Notes 123, 341—374, Longman Sci. Techn., Harlow, 1986.Google Scholar
16. Rosenberg, J. and Stolz, S., Manifolds of positive scalar curvature. In: Algebraic topology and its applications, (eds. Carlson, G.E., Cohen, R.L., Hsiang, W.C., and Jones, J.D.S.), Springer Verlag, 1994.241-267.Google Scholar
17. Schoen, R. and Yau, S.T., The structure of manifolds with positive scalar curvature, Manuscripta Math. 28(1979), 159–183.Google Scholar
18. Stolz, S., Concordance classes of positive scalar curvature metrics, in preparation.Google Scholar
19. Wolf, J., Spaces of constant curvature (5th ed.). Publish or Perish Press, Wilmington, 1985.Google Scholar
20. Wimp, J., Associated Jacobi polynomials and some applications, Canad. J. Math. 39(1987), 983—1000.Google Scholar