On the umbilicity of complete linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Lorentz space

Abstract

In this paper, we study complete linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Lorentz space. By applying some generalized maximum principles to a suitable Cheng–Yau modified operator, we establish sufficient conditions which assure that such a spacelike hypersurface must be a totally umbilical hypersurface of the ambient space.