The object of the paper is to study some properties of the generalized Einstein tensor GX,Y which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds PRSn. Considering the generalized Einstein tensor GX,Y as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of GX,Y to be symmetric.

The object of the present paper is to study weakly symmetric manifolds admitting a type of semi-symmetric non-metric connection.

No abstract

The object of the paper is to study the compatibility of [Formula: see text]-vector fields on almost pseudo-Ricci symmetric manifolds, briefly [Formula: see text]. First, we show the existence of an [Formula: see text] whose basic vector field [Formula: see text] is a [Formula: see text]-vector field by constructing a non-trivial example. Then, we investigate  the properties of the Riemann and Weyl compatibility of [Formula: see text] under certain conditions. We consider an [Formula: see text] space-time whose basic vector fields [Formula: see text] and [Formula: see text] is [Formula: see text]-vector fields of constant length. Moreover, we show that an [Formula: see text] space-time whose Ricci tensor is of Codazzi type and basic vector field [Formula: see text] is [Formula: see text]-vector field is purely electric space-time.

In this paper, we focus on an almost contact metric manifold admitting a type of semi-symmetric nonmetric connection. We find the expression for the curvature tensor of such a manifold. Furhermore, we study the properties of the curvature tensor and the projective curvature tensor.