CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY KAEHLER MANIFOLDS

- Journal title : Journal of the Korean Mathematical Society
- Volume 46, Issue 5, 2009, pp.979-995
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2009.46.5.979

Title & Authors

CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY KAEHLER MANIFOLDS

Al-Luhaibi, Nadia S.; Al-Solamy, Falleh R.; Khan, Viqar Azam;

Al-Luhaibi, Nadia S.; Al-Solamy, Falleh R.; Khan, Viqar Azam;

Abstract

As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

Keywords

nearly Kaehler manifold;CR-submanifold;CR-warped product submanifold;canonical structure;generalized complex space form;

Language

English

Cited by

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