SOME RIGIDITY THEOREMS IN SEMI-RIEMANNIAN WARPED PRODUCTS

被引：12

作者：

Colares, Antonio Gervasio ^{[1
]}

De Lima, Henrique Fernandes ^{[2
]}

机构：

[1] Univ Fed Ceara, Dept Math, BR-60455760 Fortaleza, Ceara, Brazil

[2] Univ Fed Campina Grande, Dept Matemat Estat, BR-58109970 Campina Grande, Paraiba, Brazil

来源：

KODAI MATHEMATICAL JOURNAL | 2012年 / 35卷 / 02期

关键词：

Semi-Riemannian manifolds; hyperbolic-type spaces; steady state-type spacetimes; spacelike hypersurfaces; r-th mean curvatures; CONSTANT MEAN-CURVATURE; COMPLETE SPACELIKE HYPERSURFACES; ROBERTSON-WALKER SPACETIMES; SCALAR CURVATURE; UNIQUENESS; MANIFOLDS;

D O I：

10.2996/kmj/1341401051

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 hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm. By applying a maximum principle at the infinity due to S. T. Yau and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region where the hypersurface is contained, we obtain rigidity theorems in such ambient spaces. Applications to the hyperbolic and the steady state spaces are given.

引用

页码：268 / 282

页数：15

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