NEW CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN THE DE SITTER SPACE

被引：10

作者：

Alias, Luis J. ^{[1
]}

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

dos Santos, Fabio R. ^{[2
]}

机构：

[1] Univ Murcia, Dept Matemat, Campus Espinardo, Murcia, Spain

[2] Univ Fed Campina Grande, Dept Matemat, Campina Grande, PB, Brazil

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2018年 / 292卷 / 01期

关键词：

de Sitter space; linear Weingarten hypersurfaces; spacelike hypersurfaces; totally umbilical hypersurfaces; hyperbolic cylinders; parabolicity; CONSTANT MEAN-CURVATURE;

D O I：

10.2140/pjm.2018.292.1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deal with complete linear Weingarten spacelike hypersurfaces immersed in the de Sitter space, that is, spacelike hypersurfaces of de Sitter space whose mean and scalar curvatures are linearly related. In this setting, we apply a suitable extension of the generalized maximum principle of Omori-Yau to show that either such a spacelike hypersurface must be totally umbilical or there holds a sharp estimate for the norm of its total umbilicity tensor, with equality characterizing hyperbolic cylinders of de Sitter space. We also study the parabolicity of these spacelike hypersurfaces with respect to a Cheng-Yau modified operator.

引用

页码：1 / 19

页数：19

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