Some rigidity theorems in semi-Riemannian warped products

Abstract

We study the problem of uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm. By applying a maximum principle at the infinity due to S. T. Yau and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region where the hypersurface is contained, we obtain rigidity theorems in such ambient spaces. Applications to the hyperbolic and the steady state spaces are given.