Some Hypersurfaces of Symmetric Spaces
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 303-311
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Matsuyama, Yoshio. Some Hypersurfaces of Symmetric Spaces. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 303-311. doi: 10.4153/CMB-1983-049-3
@article{10_4153_CMB_1983_049_3,
author = {Matsuyama, Yoshio},
title = {Some {Hypersurfaces} of {Symmetric} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {303--311},
year = {1983},
volume = {26},
number = {3},
doi = {10.4153/CMB-1983-049-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-049-3/}
}
[1] 1. Chen, B. Y. and Nagano, T., Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978) 405-425. Google Scholar
[2] 2. Chen, B. Y. and Verstraelen, L., Hypersurfaces of symmetric spaces, Bull. Inst. Math. Acad. Sinica 8 (1980) 201-236. Google Scholar
[3] 3. Helgason, S., Differential geometry and symmetric spaces, Academic Press, New York (1962). Google Scholar
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