Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms

Abstract

In this article, we deal with complete linear Weingarten spacelike hypersurfaces (that is, complete spacelike hypersurfaces whose mean and scalar curvatures are linearly related) immersed in a Lorentz space form. By assuming that the mean curvature attains its maximum and supposing appropriated restrictions on the norm of the traceless part of the second fundamental form, we apply Hopf's strong maximum principle in order to prove that such a spacelike hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.