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arXiv · 1401.3327

A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products

Marie-Amelie Lawn·Miguel Ortega
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Abstract

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions to construct foliations of marginally trapped surfaces in a four-dimensional Lorentzian spacetimes. We point out that, sometimes, Gauss and Codazzi equations are not sufficient to ensure the existence of a local isometric immersion of a semi-Riemannian manifold as a hypersurface of another manifold. We finally give two low-dimensional examples to illustrate our results.

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BibTeXRIS

Marie-Amelie Lawn, Miguel Ortega. 2014-01-14. A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products. https://doi.org/10.1016/j.geomphys.2015.01.002

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