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Conformally flat hypersurfaces of symmetric spaces

Part of: Classical differential geometry Global 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
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Abstract

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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

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[4]Matsuyama, Y., ‘Some hypersurfaces of symmetric spaces’, Canad. Math. Bull. 28 (1983), 303–311.CrossRefGoogle Scholar