Hypersurfaces of a Lorentz space form
β Scribed by Qing -Ming Cheng
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 477 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0003-889X
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## Abstract We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4βdimensional space forms (Β© 2010 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
We give an estimate for the Ricci curvature of a complete hypersurface M in a hyperbolic space H and in a sphere S under the same condition. As its application, we give the condition for unboundedness of a complete hypersurface M.
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