A fundamental theorem for hypersurfaces in semi-Riemannian warped products

JOURNAL OF GEOMETRY AND PHYSICS

卷:90

Article

Lawn, Marie-Amelie¹  Ortega, Miguel² 

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Granada, Fac Sci, Dept Geometry & Topol, E-18071 Granada, Spain

关键词: Fundamental theorem;    Structure equations;    Warped product;    Hypersurface;    Semi-Riemannian manifolds;   

DOI  :  10.1016/j.geomphys.2015.01.002

来源: Elsevier

【 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.

【 授权许可】

Free