Displaying similar documents to “Pseudo-parallel submanifolds of a space form.”

Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Qiaoling Wang, Chang Yu Xia (2007)

Czechoslovak Mathematical Journal

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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.