• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-995
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• 2009

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.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.239-258
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• 2021

In the present paper, we introduce the study of slant lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving some geometric results for the existence of slant lightlike submanifolds of indefinite nearly Kaehler manifolds, we give a non-trivial example of this class of lightlike submanifolds. Then, we derive some conditions for the integrability of the distributions associated with slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Consequently, we study totally umbilical slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Subsequently, we investigate minimal slant lightlike submanifolds of indefinite nearly Kaehler manifolds.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.179-194
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• 2022

In the present study, we investigate generic lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving the existence of generic lightlike submanifolds in an indefinite generalized complex space form, a non-trivial example of this class of submanifolds is discussed. Then, we find a characterization theorem enabling the induced connection on a generic lightlike submanifold to be a metric connection. We also derive some conditions for the integrability of distributions defined on generic lightlike submanifolds. Further, we discuss the non-existence of mixed geodesic generic lightlike submanifolds in a generalized complex space form. Finally, we investigate totally umbilical generic lightlike submanifolds and minimal generic lightlike submanifolds of an indefinite nearly Kaehler manifold.