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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Main Author: M. A. Bashir
Format: Article
Language:English
Published: Wiley 1993-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S016117129300050X
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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.
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issn 0161-1712
1687-0425
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publishDate 1993-01-01
publisher Wiley
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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