A fundamental theorem for hypersurfaces in semi-Riemannian warped products

作者：Lawn Marie Amelie; Ortega Miguel^*

来源：Journal of Geometry and Physics, 2015, 90: 55-70.

DOI：10.1016/j.geomphys.2015.01.002

• Fundamental theorem
• Structure equations
• Warped product
• Hypersurface
• Semi-Riemannian manifolds

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.

• 出版日期2015-4