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 |
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University of Extremadura
2017-06-01
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| Series: | Extracta Mathematicae |
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| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/386 |
| _version_ | 1819228284904275968 |
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| author | Jogli G. Araújo Henrique F. de Lima Fábio R. dos Santos Marco Antonio Velásquez |
| author_facet | Jogli G. Araújo Henrique F. de Lima Fábio R. dos Santos Marco Antonio Velásquez |
| author_sort | Jogli G. Araújo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T10:54:50Z |
| format | Article |
| id | doaj.art-bc8a10abbd3b443aad41d8cc526cc926 |
| institution | Directory Open Access Journal |
| issn | 0213-8743 2605-5686 |
| language | English |
| last_indexed | 2024-12-23T10:54:50Z |
| publishDate | 2017-06-01 |
| publisher | University of Extremadura |
| record_format | Article |
| series | Extracta Mathematicae |
| spelling | doaj.art-bc8a10abbd3b443aad41d8cc526cc9262022-12-21T17:49:48ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862017-06-01321Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian ManifoldJogli G. Araújo0Henrique F. de Lima1Fábio R. dos Santos2Marco Antonio Velásquez3Departamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, BrazilDepartamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, BrazilDepartamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, BrazilDepartamento de Matemática, Universidade Federal de Campina Grande, 58.429 − 970 Campina Grande, Paraı́ba, BrazilIn 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.https://publicaciones.unex.es/index.php/EM/article/view/386Locally symmetric semi-Riemannian manifoldcomplete linear Weingarten spacelike submanifoldsisoparametric submanifolds |
| spellingShingle | Jogli G. Araújo Henrique F. de Lima Fábio R. dos Santos Marco Antonio Velásquez Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold Extracta Mathematicae Locally symmetric semi-Riemannian manifold complete linear Weingarten spacelike submanifolds isoparametric submanifolds |
| title | Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold |
| title_full | Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold |
| title_fullStr | Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold |
| title_full_unstemmed | Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold |
| title_short | Characterizations of Complete Linear Weingarten Spacelike Submanifolds in a Locally Symmetric Semi-Riemannian Manifold |
| title_sort | characterizations of complete linear weingarten spacelike submanifolds in a locally symmetric semi riemannian manifold |
| topic | Locally symmetric semi-Riemannian manifold complete linear Weingarten spacelike submanifolds isoparametric submanifolds |
| url | https://publicaciones.unex.es/index.php/EM/article/view/386 |
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