Complete hypersurfaces in the space form with three principal curvatures
β Scribed by Reiko Miyaoka
- Publisher
- Springer-Verlag
- Year
- 1982
- Tongue
- French
- Weight
- 506 KB
- Volume
- 179
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
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
## Abstract In this paper we study complete orientable surfaces with a constant principal curvature __R__ in the 3βdimensional hyperbolic space **H**^3^. We prove that if __R__^2^ > 1, such a surface is totally umbilical or umbilically free and it can be described in terms of a complete regular cur
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.