In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, D -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained. D

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F -invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1)×M2(c2) M.S.C...

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

Warped product CR-submanifolds in Kählerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen in [2], [3]. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kählerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds (cf. [6], [7]). In this n...

In the present paper we study lightlike submanifolds of almost paracontact metric manifolds. We define invariant lightlike submanifolds. We study radical transversal lightlike submanifolds of para-Sasakian manifolds and investigate the geometry of distributions. Also we introduce a general notion of paracontact Cauchy-Riemann (CR) lightlike submanifolds and we derive some necessary and sufficie...

We first prove some results on invariant lightlike submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR) lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR) lightlike submanifolds which include invariant and screen real subcases. Finally, we ...

Recently, we researched certain twisted product CR-submanifolds in a Kaehler manifold and some inequalities of the second fundamental form of this submanifold ([11]). In this talk, we consider two kind twisted product CR-submanifolds in a locally conformal Kaehler manifold. In these submanifolds, we give a inequality of the second fundamental form (See Theorems 5.3 and 5.4) and consider the equ...

In this article we investigate the geometry of CR-lightlike submanifolds in an indefinite Kähler product manifold. In particular, we obtain the necessary and sufficient conditions for a CR-lightlike submanifold in an indefinite Kähler product manifold to be either CR-lightlike product, or D-geodesic, or D′-geodesic. We also study totally umbilical and curvature-invariant CR-lightlike submanifol...

We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It means every admissible deformation of the submanifold osculates a one parameter family of motions up to 1st order. We implement this idea to the question...