GENERALIZED CAUCHY-RIEMANN SCREEN PSEUDO-SLANT LIGHTLIKE SUBMANIFOLDS OF INDEFINITE SASAKIAN MANIFOLDS

This paper deals with the study of generalized Cauchy-Riemann (in short, GCR) screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds giving a characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2, D′1 and D′2 on GCR screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Furthermore, we obtain necessary and sufficient conditions for foliations determined by the above distributions to be totally geodesic

GCR

We study mixed geodesic GCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product

Lightlike Submanifolds of Indefinite Sasakian Manifolds

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 prove characterization theorems on the existence of contact SCR, screen real, invariant, and contact CR minimal lightlike submanifolds

Totally Contact Umbilical Radical Transversal Lightlike Submanifolds Of An Almost Contact Manifold With B-Metric

In the present paper, we study the geometry of totally contact umbilical radical transversal lightlike submanifolds and totally contact umbilical CR- submanifold of an indenite Sasaki-like almost contact manifold with B-metric. We nd the necessary and sucient condition for the characterization of the induced connection to be a metric connection. Finally, we have proved that for a totally contact umbilical CR-submanifold, totally contact umbilical radical transversal lightlike submanifold is a totally geodesic radical transversal lightlike submanifold