Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold
Palabras clave:
Locally symmetric semi-Riemannian manifold, complete linear Weingarten spacelike submanifolds, isoparametric submanifoldsResumen
In this paper, we deal with n-dimensional complete spacelike submanifolds M n with flat normal bundle and parallel normalized mean curvature vector immersed in an (n + p)-dimensional locally symmetric semi-Riemannian manifold Ln+pp 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 M n is isometric to an isoparametric hypersurface of Ln+11 having two distinct principal curvatures, one of which is simple.
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