Rigidity of complete spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimes

摘要

Our purpose in this paper is to apply some maximum principles in order to study the rigidity of complete spacelike hypersurfaces immersed in a spatially weighted generalized Robertson Walker (GRW) spacetime, which is supposed to obey the so called strong null convergence condition. Under natural constraints on the weight function and on the f-mean curvature, we establish sufficient conditions to guarantee that such a hypersurface must be a slice of the ambient spacetime. In this setting, we also obtain new Calabi Bernstein type results concerning entire graphs in a spatially weighted GRW spacetime. (C) 2016 Elsevier B.V. All rights reserved.