On the geometry of linear Weingarten spacelike hypersurfaces in the de Sitter space

被引：10

作者：

de Lima, Henrique F. ^{[1
]}

Velasquez, Marco A. L. ^{[1
]}

机构：

[1] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58429970 Campina Grande, PB, Brazil

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2013年 / 44卷 / 01期

关键词：

de Sitter space; spacelike hypersurfaces; linear Weingarten hypersurfaces; totally umbilical hypersurfaces; hyperbolic cylinder; CONSTANT SCALAR CURVATURE; MEAN-CURVATURE;

D O I：

10.1007/s00574-013-0003-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our purpose is to study the geometry of linear Weingarten spacelike hypersurfaces immersed in the de Sitter space . In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of the hyperbolic cylinders of . In the compact case, we obtain a rigidity result concerning to a such hypersurface according to the length of its second fundamental form.

引用

页码：49 / 65

页数：17

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