Compact space-like hypersurfaces in de Sitter space.

Lv, Jinchi

Displaying similar documents to “Compact space-like hypersurfaces in de Sitter space.”

Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature.

Cai, Kairen, Xu, Huiqun (2006)

International Journal of Mathematics and Mathematical Sciences

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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.

Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space $H_{1}^{n + 1} (- 1)$

Guoxin Wei, Qiuli Liu, Young Jin Suh (2009)

Czechoslovak Mathematical Journal

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In this paper, we study closed $k$ -maximal spacelike hypersurfaces $M^{n}$ in anti-de Sitter space $H_{1}^{n + 1} (- 1)$ with two distinct principal curvatures and give some integral formulas about these hypersurfaces.

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.

Curvature conditions on hypersurfaces with two distinct principal curvatures

Małgorzata Głogowska (2005)

Banach Center Publications

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We investigate curvature properties of hypersurfaces in semi-Riemannian spaces of constant curvature with the minimal polynomial of the second fundamental tensor of second degree. We present suitable examples of hypersurfaces.

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.

The geometry of closed hypersurfaces

Sebastião de Almeida, Fabiano Brito (1987-1988)

Séminaire de théorie spectrale et géométrie

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Complete hypersurfaces with constant scalar curvature in a sphere

Ximin Liu, Hongxia Li (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, by using Cheng-Yau’s self-adjoint operator $□$ , we study the complete hypersurfaces in a sphere with constant scalar curvature.