On the umbilicity of complete constant mean curvature spacelike hypersurfaces |
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Authors: | Cícero P Aquino Henrique F de Lima |
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Institution: | 1. Departamento de Matemática, Universidade Federal do Piauí, Teresina, Piauí, 64049-550, Brazil 2. Departamento de Matemática, Universidade Federal de Campina Grande, Campina Grande, Paraíba, 58429-970, Brazil
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Abstract: | In this paper, we show that a complete spacelike hypersurface immersed with constant mean curvature either in the de Sitter space or in the anti-de Sitter space must be totally umbilical, provided that its Gauss mapping has some suitable behavior. In particular, we use an extension of Hopf’s maximum principle due to Yau in order to give new positive answers to Goddard’s conjecture. |
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