Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space |
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Authors: | Qiaoling Wang Changyu Xia |
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Institution: | (1) Departamento de Matemática-IE, Universidade de Brasília, Campus Universitário, 70910-900 Brasília-DF, Brasil |
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Abstract: | In this paper we study the topological and metric rigidity of hypersurfaces in ℍ
n+1, the (n + 1)-dimensional hyperbolic space of sectional curvature −1. We find conditions to ensure a complete connected oriented hypersurface
in ℍ
n+1 to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface
with constant norm of the second fundamental form to be totally umbilic. |
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Keywords: | rigidity hypersurfaces topology hyperbolic space |
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