The purpose of the paper is to introduce the notion of generalized recurrent Lorentzian transSasakian manifold and study some of the properties of generalized recurrent and Ricci recurrent Lorentzian Trans-Sasakian manifolds.

The object of the present paper is to study generalized φ− recurrent and generalized concircular φ− recurrent P-Sasakian manifold. AMS Mathematics Subject Classification (2010): 53B20, 53D15.

In the present work, generalized recurrent and concircularly Weyl manifolds are examined. We define nearly quasi-Einstein we proved that if a or manifold admits special concircular vector field, then reduces to manifold. Also, some other results presented.

The purpose of this study is to evaluate the curvature tensor and Ricci a P-Sasakian manifold with respect quarter-symmetric metric connection on tangent bundle TM. Certain results semisymmetric manifold, generalized recurrent manifolds, pseudo-symmetric manifolds TM are proved.

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally recurrent manifold is shown to be either a de Sitter space or an anti-de space. In particular, spacetime must spacetime.