Bernstein type results for complete spacelike hypersurfaces immersed in a weighted conformally stationary spacetime

Abstract

In this paper, we deal with complete noncompact spacelike hypersurfaces immersed in a weighted conformally stationary spacetime endowed with a closed conformal timelike vector field [Formula: see text]. Under suitable constraints on the weighted mean curvature of such a spacelike hypersurface, we establish sufficient conditions to ensure that it must be an integral leaf of the foliation orthogonal to [Formula: see text].