On the rigidity of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime

被引：19
|
作者：
Alias, Luis J. [1 ]
Colares, Antonio Gervasio [2 ]
de Lima, Henrique F. [3 ]
机构：
[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
[3] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58109970 Campina Grande, PB, Brazil
来源：
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2013年 / 44卷 / 02期
关键词：
generalized Robertson-Walker spacetimes; null convergence condition; complete spacelike hypersurface; entire vertical graphs; mean curvature; CONSTANT MEAN-CURVATURE; UNIQUENESS; SURFACES;
D O I：
10.1007/s00574-013-0009-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the problem of uniqueness of complete noncompact spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime, which is supposed to satisfy the so-called null convergence condition. By extending a technique of S.T. Yau and imposing a suitable restriction on the norm of the gradient of the height function of the hypersurface, we obtain rigidity theorems in such ambient spacetimes. Furthermore, we also establish nonparametric results concerning entire vertical graphs.
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页码：195 / 217
页数：23
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