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Displaying similar documents to “Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space H 1 n + 1 ( - 1 ) ”

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.

Characterization of totally umbilic hypersurfaces in a space form by circles

Toshiaki Adachi, Sadahiro Maeda (2005)

Czechoslovak Mathematical Journal

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In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.

On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)

Colloquium Mathematicae

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We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.