Fundamental Equations of Generalized φ(Ric)-Vector Fields

Abstract

The paper treats pseudo-Riemannian spaces admitting generalized \(\varphi\)(Ric)-vector fields. We investigate the fundamental equations governing the existence of such vector fields, which are expressed as closed linear partial equations of the Cauchy type. In particular, we examine these equations within the context of constant curvature and Kähler spaces.