Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds
We study totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000668 |
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| _version_ | 1832548807597883392 |
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| author | K. L. Duggal R. Sharma |
| author_facet | K. L. Duggal R. Sharma |
| author_sort | K. L. Duggal |
| collection | DOAJ |
| description | We study totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel. |
| format | Article |
| id | doaj-art-3634bced9b8f486d89026b234af17fc0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3634bced9b8f486d89026b234af17fc02025-02-03T06:12:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110355155510.1155/S0161171287000668Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifoldsK. L. Duggal0R. Sharma1Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B 3P4, CanadaDepartment of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B 3P4, CanadaWe study totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.http://dx.doi.org/10.1155/S0161171287000668CR-submanifoldstotally umbilicalsemi-Riemannian metricKaehler manifoldnormal contact metric structuresecond fundamental form. |
| spellingShingle | K. L. Duggal R. Sharma Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds International Journal of Mathematics and Mathematical Sciences CR-submanifolds totally umbilical semi-Riemannian metric Kaehler manifold normal contact metric structure second fundamental form. |
| title | Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds |
| title_full | Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds |
| title_fullStr | Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds |
| title_full_unstemmed | Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds |
| title_short | Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds |
| title_sort | totally umbilical cr submanifolds of semi riemannian kaehler manifolds |
| topic | CR-submanifolds totally umbilical semi-Riemannian metric Kaehler manifold normal contact metric structure second fundamental form. |
| url | http://dx.doi.org/10.1155/S0161171287000668 |
| work_keys_str_mv | AT klduggal totallyumbilicalcrsubmanifoldsofsemiriemanniankaehlermanifolds AT rsharma totallyumbilicalcrsubmanifoldsofsemiriemanniankaehlermanifolds |