On totally umbilical CR-submanifolds of a Kaehler manifold
Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or RP3 or a lens space Lp,q3.
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129300050X |
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| _version_ | 1850159907427319808 |
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| author | M. A. Bashir |
| author_facet | M. A. Bashir |
| author_sort | M. A. Bashir |
| collection | DOAJ |
| description | Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler
manifold of positive holomorphic sectional curvature. We prove that if the length of the mean
curvature vector of M does not vanish, then M is either diffeomorphic to S3 or RP3 or a lens space
Lp,q3. |
| format | Article |
| id | doaj-art-b22b9f65cf994323b8ac29b5ac51bf94 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b22b9f65cf994323b8ac29b5ac51bf942025-08-20T02:23:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116240540810.1155/S016117129300050XOn totally umbilical CR-submanifolds of a Kaehler manifoldM. A. Bashir0Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaLet M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or RP3 or a lens space Lp,q3.http://dx.doi.org/10.1155/S016117129300050XCR-submanifolds. totally umbilical submanifolds. Kaehler manifold. |
| spellingShingle | M. A. Bashir On totally umbilical CR-submanifolds of a Kaehler manifold International Journal of Mathematics and Mathematical Sciences CR-submanifolds. totally umbilical submanifolds. Kaehler manifold. |
| title | On totally umbilical CR-submanifolds of a Kaehler manifold |
| title_full | On totally umbilical CR-submanifolds of a Kaehler manifold |
| title_fullStr | On totally umbilical CR-submanifolds of a Kaehler manifold |
| title_full_unstemmed | On totally umbilical CR-submanifolds of a Kaehler manifold |
| title_short | On totally umbilical CR-submanifolds of a Kaehler manifold |
| title_sort | on totally umbilical cr submanifolds of a kaehler manifold |
| topic | CR-submanifolds. totally umbilical submanifolds. Kaehler manifold. |
| url | http://dx.doi.org/10.1155/S016117129300050X |
| work_keys_str_mv | AT mabashir ontotallyumbilicalcrsubmanifoldsofakaehlermanifold |