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 ap
Spacelike hypersurfaces in de Sitter space
β Scribed by Hua-Dong Pang; Sen-Lin Xu; Shu Dai
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 53 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0393-0440
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β¦ Synopsis
In this paper, we give one intrinsic inequality for spacelike hypersurfaces in de Sitter space and a sufficient and necessary condition for such hypersurfaces to be totally geodesic.
π SIMILAR VOLUMES
It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if one of the mean curvatures H l does not vanish and the ratio H k /H l is constant for some k, l, 1 β€ l < k β€ n. This exte
In this paper, we develop a series of general integral formulae for compact spacelike hypersurfaces with hyperplanar boundary in the (n + 1)-dimensional Minkowski space-time L n+1 . As an application of them, we prove that the only compact spacelike hypersurfaces in L n+1 having constant higher orde
To each immersed complete space-like hypersurface M with constant normalized scalar curvature R in the de Sitter space S n+1 1 , we associate sup H 2 , where H is the mean curvature of M. It is proved that the condition sup H 2 β€ C n ( R), where R = (R -1) > 0 and C n ( R) is a constant depending on