A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products Ortega, Miguel Lawn, Marie-Amélie Differential geometry General relativity and quantum cosmology Mathematical physics We give necessary and sufficient conditions for a semi-Riemannian manifold of arbi- trary signature to be locally isometrically immersed into a warped product ±I ×a M^n (c), where I ⊂ R and M^n (c) is a semi-Riemannian space of constant nonzero sectional cur- vature. 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 space- times. 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. 2014-01-17T07:21:28Z 2014-01-17T07:21:28Z 2014-01-14 info:eu-repo/semantics/preprint arXiv:1401.3327v1 http://hdl.handle.net/10481/29868 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License