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Curvature properties of compact spacelike hypersurfaces in de Sitter space

✍ Scribed by Juan A. Aledo; Luis J. Alı́as

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
87 KB
Volume
14
Category
Article
ISSN
0926-2245

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✦ Synopsis

In this paper we establish a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a lower bound for the square of its mean curvature. Our result will be a consequence of the maximum principle for the Laplacian operator. We also derive some other applications and consequences of our main result. In particular, we establish another sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a pinching condition for its scalar curvature, as well as in terms of the Ricci curvature and in terms of the higher order mean curvatures.

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