New Calabi–Bernstein type results in Lorentzian product spaces with density. (August 2020) - Aquino, Cícero P.; Baltazar, Halyson I.; de Lima, Henrique F.
Abstract: We investigate the rigidity of complete spacelike hypersurfaces immersed in a weighted Lorentzian product space of the type R 1 × P f n, endowed with a weight function f which does not depend on the parameter t ∈ R and whose Riemannian fiber P n has nonnegative Bakry–Émery–Ricci tensor. In this direction, supposing that the f -mean curvature is constant and assuming appropriate constraints on the norm of the gradient of f, we prove that such a spacelike hypersurface must be a slice of the ambient space. As application of our investigation, we obtain new Calabi–Bernstein type results concerning entire spacelike graphs constructed over P n . Our approach is based on an extension for the drift Laplacian of a generalized maximum principle of Akutagawa (1987) and a Liouville-type result due to Pigola et al. (2005).