The index of constant mean curvature surfaces in hyperbolic 3-space
✍ Scribed by P. Bérard; M. do Carmo; W. Santos
- Publisher
- Springer-Verlag
- Year
- 1997
- Tongue
- French
- Weight
- 247 KB
- Volume
- 224
- Category
- Article
- ISSN
- 0025-5874
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📜 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 3‐dimensional 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