On the geometry of complete spacelike hypersurfaces in the anti-de Sitter space

被引：5

作者：

Aquino, Cicero P. ^{[1
]}

de Lima, Henrique F. ^{[2
]}

Velasquez, Marco Antonio L. ^{[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：

GEOMETRIAE DEDICATA | 2015年 / 174卷 / 01期

关键词：

Anti-de Sitter space; Complete spacelike hypersurfaces; Totally umbilical hypersurfaces; Totally geodesic hypersurfaces; Mean curvature; Scalar curvature; Gauss mapping; CONSTANT MEAN-CURVATURE;

D O I：

10.1007/s10711-014-0002-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by the nonexistence of closed spacelike hypersurfaces in the anti-de Sitter space , in this paper we study the geometry of complete spacelike hypersurfaces immersed in with either constant mean or scalar curvature. In this setting, under suitable restrictions on the norm of the tangential component of a fixed timelike vector, we show that such hypersurfaces must be isometric to certain hyperbolic spaces. Our approach is based on the use of Bochner's technique jointly with appropriated generalized maximum principles.

引用

页码：13 / 23

页数：11

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