On the umbilicity of generalized linear Weingarten spacelike hypersurfaces in a Lorentzian space form

Abstract

In this paper, we deal with complete generalized linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form, which means that there exists a linear relation involving some of the higher order mean curvatures. In this setting, we show that such a spacelike hypersurface must be totally umbilical, provided that its Gauss mapping has some appropriate behavior and that the tangential component of a fixed nonzero vector has integrable norm along it. Our approach is based on a suitable divergence formula jointly with an appropriate maximum principle at the infinity.