• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1173-1192
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• 2013

We introduce CR, SCR and GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature $c$ and of constant type ${\alpha}$. We also prove characterization theorems on the existence of totally umbilical and minimal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds.

• 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.