On the umbilicity of complete constant mean curvature spacelike hypersurfaces (Q476755)
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scientific article; zbMATH DE number 6375914
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the umbilicity of complete constant mean curvature spacelike hypersurfaces |
scientific article; zbMATH DE number 6375914 |
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On the umbilicity of complete constant mean curvature spacelike hypersurfaces (English)
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2 December 2014
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This paper investigates complete, space-like hypersurfaces with constant mean curvature in either de Sitter space or anti-de Sitter space. The main results provide a variety of sufficient conditions (expressed as restrictions on the Gauss map) for the immersion to be totally umbilical. In the case of anti-de Sitter space, the conditions imply both umbilicity and hyperbolicity.
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constant mean curvature
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space-like hypersurfaces
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Gauss map
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de Sitter space
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Anti-de Sitter space
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Goddard conjecture
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