A fundamental theorem for hypersurfaces in semi-Riemannian warped products

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 hypersurface 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.