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Some Hypersurfaces of Symmetric Spaces

Published online by Cambridge University Press:  20 November 2018

Yoshio Matsuyama
Yoshio Matsuyama*
Affiliation:
Department of Mathematics ChuoUniversity 1-13-27 Kasuga, Bunkyo-Ku, Tokyo, 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 hypersurface N with at most two distinct principal curvatures. Then we will obtain that (1) if N is locally symmetric, then M must be a sphere, a real projective space and their noncompact duals (2) if N is Einstein, then M must be rank 1.

Keywords

53C4053C35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 303 - 311
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Chen, B. Y. and Nagano, T., Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978) 405-425.Google Scholar
2. Chen, B. Y. and Verstraelen, L., Hypersurfaces of symmetric spaces, Bull. Inst. Math. Acad. Sinica 8 (1980) 201-236.Google Scholar
3. Helgason, S., Differential geometry and symmetric spaces, Academic Press, New York (1962).Google Scholar