Abstract
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 to a point, it is a geodesic hypercylinder; if its soul is reduced to a point p, its curvature satisfies ∥∇Q∥ < ∞, and the geodesic spheres centered at p are convex, then it is a horosphere.
Original language | English (US) |
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Pages (from-to) | 197-222 |
Number of pages | 26 |
Journal | Geometriae Dedicata |
Volume | 59 |
Issue number | 2 |
DOIs | |
State | Published - 1996 |
Externally published | Yes |
Keywords
- Hyperbolic space
- Hypersurfaces
- Ricci curvature
ASJC Scopus subject areas
- Geometry and Topology