On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space

Abstract

Our purpose in this paper is to study the geometry of complete linear Weingarten spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space, which is supposed to obey standard curvature constrains. In this setting, we apply some appropriated generalized maximum principles to a suitable Cheng-Yau modified operator in order to guarantee that such a spacelike hypersurface must be isometric to an isoparametric hypersurface of the ambient space.