Compatibility of φ(Ric)-vector fields on almost pseudo-Ricci symmetric manifolds

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.