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Hadamard-type theorems for hypersurfaces in hyperbolic spaces |
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| Authors: | Luis J Alías Takashi Kurose Gil Solanes |
| Institution: | a Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain b Department of Applied Mathematics, Fukuoka University, Nanakuma, Fukuoka 814-0180, Japan c Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 Avenue Alain Savary, BP47870, 21078 Dijon Cedex, France |
| Abstract: | We prove that a bounded, complete hypersurface in hyperbolic space with normal curvatures greater than −1 is diffeomorphic to a sphere. The completeness condition is relaxed when the normal curvatures are bounded away from −1. The diffeomorphism is constructed via the Gauss map of some parallel hypersurface. We also give bounds for the total curvature of this parallel hypersurface. |
| Keywords: | 52A55 53C40 |
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