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1. Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

Author

Rosa Maria dos Santos Barreiro Chaves, L.A.M. Sousa, and F.E.C. Camargo

Subjects
Complete spacelike hypersurfaces, Constant scalar curvature, De Sitter space, Prescribed scalar curvature problem, Mathematical analysis, Curvature, General Relativity and Quantum Cosmology, Hypersurface, Computational Theory and Mathematics, GEOMETRIA DIFERENCIAL, Mathematics::Differential Geometry, Anti-de Sitter space, Geometry and Topology, Constant (mathematics), de Sitter invariant special relativity, Analysis, Scalar curvature, Mathematical physics, Mathematics
Abstract

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S 1 n + 1 ( c ) , n ⩾ 3 , with constant normalized scalar curvature R satisfying n − 2 n c ⩽ R ⩽ c totally umbilical?

Published
2008
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