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Title: Characterizations of complete linear Weingarten spacelike submanifolds in a locally symmetric semi-Riemannian manifold
Authors: Araújo, Jogli G.
Lima, Henrique F. de
Santos, Fábio R. dos
Velásquez, Marco Antonio L.
Keywords: Locally symmetric semi-Riemannian manifold;Complete linear Weingarten spacelike submanifolds;Isoparametric submanifolds;Colector semi-Riemannian localmente simétrico;Forma de espacio de Weingarten lineal completo
Issue Date: 2017
Publisher: Universidad de Extremadura
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.
Appears in Collections:Extracta Mathematicae Vol. 32, nº 1 (2017)

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