Characterizations of complete linear Weingarten spacelike submanifolds in a locally symmetric semi-Riemannian manifold

Abstract

In this paper, we deal with n-dimensional complete spacelike submanifolds Mn with flat normal bundle and parallel normalized mean curvature vector immersed in an (n + p)-dimensional locally symmetric semi-Riemannian manifold L_p^(n+p) of index p obeying some standard curvature conditions which are naturally satisfied when the ambient space is a semi-Riemannian space form. In this setting, we establish sufficient conditions to guarantee that, in fact, p = 1 and Mⁿ is isometric to an isoparametric hypersurface of L_1^(n+1)having two distinct principal curvatures, one of which is simple.