Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

Abstract

The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.