Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold
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 natu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Extremadura
2017-06-01
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| Series: | Extracta Mathematicae |
| Subjects: | |
| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/386 |
| Summary: | 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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| ISSN: | 0213-8743 2605-5686 |