In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced
β¦ LIBER β¦
Compact Hopf hypersurfaces of constant mean curvature in complex space forms
β Scribed by Vicente Miquel
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 335 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0232-704X
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It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if one of the mean curvatures H l does not vanish and the ratio H k /H l is constant for some k, l, 1 β€ l < k β€ n. This exte