A fundamental theorem for hypersurfaces in semi-Riemannian warped products

被引：15
|
作者：
Lawn, Marie-Amelie [1 ]
Ortega, Miguel [2 ]
机构：
[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
[2] Univ Granada, Fac Sci, Dept Geometry & Topol, E-18071 Granada, Spain
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2015年 / 90卷
关键词：
Fundamental theorem; Structure equations; Warped product; Hypersurface; Semi-Riemannian manifolds; ISOMETRIC IMMERSIONS; SURFACES;
D O I：
10.1016/j.geomphys.2015.01.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find necessary and sufficient conditions for nondegenerate arbitrary signature manifolds to be realized as hypersurfaces in a large class of warped products manifolds. As an application, we give conditions for a 3-dimensional hypersurfaces in a 4-dimensional Robertson-Walker spacetime to be foliated by surfaces with lightlike or zero mean curvature and hence describe a way to study horizons in such spacetimes. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：55 / 70
页数：16
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