Abstract
In this paper we study the topological and metric rigidity of hypersurfaces in ℍn+1, the (n + 1)-dimensional hyperbolic space of sectional curvature −1. We find conditions to ensure a complete connected oriented hypersurface in ℍn+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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Wang, Q., Xia, C. Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space. Czech Math J 57, 435–445 (2007). https://doi.org/10.1007/s10587-007-0071-7
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DOI: https://doi.org/10.1007/s10587-007-0071-7