Displaying similar documents to “Some rigidity results for spatially closed spacetimes”

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.

Construction of compact constant mean curvature hypersurfaces with topology

Mohamed Jleli (2012)

Annales de l’institut Fourier

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In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.

Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

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A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature H, for some r = 1, ..., n.