A β-tensor on Kaehler manifolds and its geometric characterizations

In this paper, we first introduce a new notion [Formula: see text]-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the [Formula: see text]-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits [Formula: see text]-Ricci soliton and [Formula: see text]-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is [Formula: see text]-Ricci soliton or [Formula: see text]-Kaehler-Einstein.

TANGENT BUNDLE ENDOWED WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION ON AN ALMOST HERMITIAN MANIFOLD

In this paper, we have studied the tangent bundle endowed with quarter-symmetric non-metric connection obtained by vertical and complete lifts of a quarter-symmetric non-metric connection on the base manifold and, also, proposed the study of the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold. Finally, we obtained some theorems for Nijenhuis tensor on the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold.\\

Some characterization theorems on GCR-lightlike warped product submanifolds of indefinite nearly Kaehler manifolds

It is shown that for a proper Generalized Cauchy–Riemann ([Formula: see text])-lightlike submanifold of an indefinite nearly Kaehler manifold such that [Formula: see text] defines a totally geodesic foliation in [Formula: see text], there does not exist any warped product [Formula: see text]-lightlike submanifold of the type [Formula: see text]. Then, the existence of [Formula: see text]-lightlike warped product submanifolds of the type [Formula: see text] in indefinite nearly Kaehler manifolds is obtained by establishing a characterization in terms of the shape operator. Further, we prove that for a proper [Formula: see text]-lightlike warped product submanifold of an indefinite nearly Kaehler manifold, the induced connection [Formula: see text] can never be a metric connection. Finally, we derive some characterizations in terms of the canonical structures [Formula: see text] and [Formula: see text] on a [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold enabling it to be a [Formula: see text]-lightlike warped product.

Radical screen transversal slant lightlike submanfolds of indefinite Kaehler manifolds

In this paper, we define Radical screen transversal slant lightlike submanifolds of an indefinite Kaehler manifold and give an example. We prove two characterization theorems for the existence of the Radical screen transversal slant lightlike submanifolds and obtain the necessary and su_cient conditions for Radical screen transversal slant lightlike submanifolds to be Radical screen slant lightlike product.

RADICAL TRANSVERSAL SCR-LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS

In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)-lightlike submanifolds of indefinite Kaehler manifolds giving a charac-terization theorem with some non-trivial examples of such submanifolds. Integrabilityconditions of distributions D1, D2, D and D? on radical transversal SCR-lightlike sub-manifolds of an indefinite Kaehler manifold have been obtained. Further, we obtainnecessary and sufficient conditions for foliations determined by the above distributionsto be totally geodesic.

Geometry of semi-transversal lightlike warped product submanifolds of indefinite Kaehler manifolds

In this paper, we investigate warped product semi-transversal lightlike submanifolds of indefinite Kaehler manifolds. It is shown that there does not exist any warped product semi-transversal lightlike submanifold of the type [Formula: see text] in an indefinite Kaehler manifold. Moreover, a necessary and sufficient condition for an isometrically immersed semi-transversal lightlike submanifold of an indefinite Kaehler manifold to be a semi-transversal lightlike warped product of the type [Formula: see text] is obtained, in terms of the shape operator.

Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

We study lightlike hypersurfaces M of an indefinite Kaehler manifold M̅ of quasi-constant curvature subject to the condition that the characteristic vector field ζ of M̅ is tangent to M. First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface M of M̅ such that(1) the screen distribution S(TM) is totally umbilical or(2) M is screen conformal.

Some results on normal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds

The purpose of this paper is to study normal [Formula: see text]-lightlike submanifolds of indefinite nearly Kaehler manifolds. We find some necessary and sufficient conditions for an isometrically immersed [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold to be a normal [Formula: see text]-lightlike submanifold. Further, we derive a characterization theorem for holomorphic bisectional curvature of a normal [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold.