On the umbilicity of complete constant mean curvature spacelike hypersurfaces

被引：13
|
作者：
Aquino, Cicero P. [1 ]
de Lima, Henrique F. [2 ]
机构：
[1] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil
[2] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
来源：
MATHEMATISCHE ANNALEN | 2014年 / 360卷 / 3-4期
关键词：
GAUSS MAP; SITTER SPACE; EXISTENCE; RIGIDITY; IMAGE;
D O I：
10.1007/s00208-014-1049-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：555 / 569
页数：15
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