Hostname: page-component-7bb8b95d7b-2h6rp Total loading time: 0 Render date: 2024-09-06T22:52:59.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Conformally flat hypersurfaces of symmetric spaces

Part of: Global differential geometry Classical differential geometry

Published online by Cambridge University Press:  09 April 2009

Yoshio Matsuyama
Yoshio Matsuyama
Affiliation:
Department of Mathematics Chuo University1-13-27 Kasuga, Bunkyo-ku, Tokyo 112, Japan
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.

In this paper we consider how much we can say about an irreducible symmetric space M which admits a single hypersurface with at most two distinct principal curvatures. Then we prove that if N is conformally flat, then N is quasiumbilical and M must be a sphere, a real projective space or the noncompact dual of a sphere or a real projective space.

MSC classification

Secondary: 53C40: Global submanifolds 53C35: Symmetric spaces 53A30: Conformal differential geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Chen, B. Y., Geometry of submanifolds (M. Dekker, New York, 1973).Google Scholar
[2]Chen, B. Y. and Nagano, T., ‘Totally geodesic submanifolds of symmetric spaces, II’, Duke Math. J. 45 (1978), 405–425.CrossRefGoogle Scholar
[3]Chen, B. Y. and Verstraelen, L., ‘Hypersurfaces of symmetric spaces’, Bull. Inst. Math. Acad. Sinica 8 (1980), 201–236.Google Scholar
[4]Matsuyama, Y., ‘Some hypersurfaces of symmetric spaces’, Canad. Math. Bull. 28 (1983), 303–311.CrossRefGoogle Scholar