@misc{10481/29868,
year = {2014},
month = {1},
url = {http://hdl.handle.net/10481/29868},
abstract = {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.},
organization = {Spanish MEC-FEDER Grant MTM2007-60731 and Junta de Andalucía Grant P09-FQM-4496 (with FEDER funds.)},
keywords = {Differential geometry},
keywords = {General relativity and quantum cosmology},
keywords = {Mathematical physics},
title = {A Fundamental Theorem for Hypersurfaces in Semi-Riemannian Warped Products},
author = {Ortega, Miguel and Lawn, Marie-Amélie},
}