Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

Abstract

In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called quasi generalized Cauchy-Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable. Mathematics Subject Classification

A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds

“…Consider a quasi-orthonormal frame a long T M given by The following result for ascreen QGCR-lightlike submanifolds is wellknown (see Lemma 3.6 and Theorem 3.7 of [18]). From (4.1) and (3.1), we can write the generalized structure vector field of an ascreen QGCR-lightlike submanifold as…”

Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly Cosymplectic Manifolds

“…From the above definition, we can easily deduce the following; Proof. The proof follows from straightforward calculation as in [21].…”

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In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold.

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Some results on null hypersurfaces in $(LCS)$-manifolds

“…Their approach is extrinsic contrary to the intrinsic approach of Kupeli [18]. Based on the above books, many authors picked interest in null geometry, for instance see [1,2,5,6,9,10,11,17] and many more references cited therein.…”