CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection

Abstract

We define a semi-symmetric non-metric connection in a Lorentzian para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

Quasi hemi Slant Submanifolds of Lorentzian Concircular Structures

“…Since 𝜉 is unit concircular vector field, it follows that there exist 1-form 𝜂 which is a nonzero such that: 𝑔(𝑋, 𝜉) = 𝜂(𝑋) (4) for which the equation of the following form holds:…”

“…[1], introduced and studied the concept of Lorentzian almost paracontact manifolds. Then after, many other authors studied the Lorentzian almost paracontact manifolds, [2], [3], [4], [5], [6], [7], [8], [9], [10]. The application of (𝐿𝐶𝑆) 𝑛manifolds was investigated by [11], in the field of general theory of relativity and cosmology.…”

Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

“…[10] introduced the concept of ) , ( Özgür [11] studied the submanifolds of Riemannian manifold with semi-symmetric non-metric connection. Moreover, Özgür and others also studied the different structures with semi-symmetric non-metric connection in ( [12], [13]) . On other hand, some properties of semi-invariant submanifolds, hypersurfaces and submanifolds with semi-symmetric non-metric connection were studied in ( [14], [15], [16]).…”

CR- Submanifoldsof a Nearly Hyperbolic Cosymplectic Manifold

“…CR-submanifolds of Sasakian manifold was studied by C.J. Hsu in [3] and M. Kobayashi in [4].Later, several geometers (see, [5], [6] [7], [8] [9], [10]) enriched the study of CR-submanifolds of almost contact manifolds. On the other hand,almost hyperbolic ( , , , )-structure was defined and studied by Upadhyay and Dube in [11].…”