Gradient conformal killing vectors and exact solutions

We establish a connection between conformally related Einstein spaces and conformai killing vectors (CKV). We begin with the conformal map and prove that (a) under the conformal mapping¯g _ik=^–2g_ik, the necessary and sufficient condition for the tracefree part of the Ricci tensor (S _ik=R_ik–(R/4)g _ik) to remain invariant is that _i is a CKV ofg _ik, and (b) the most general form for for conformally flat Einstein space, which is the de Sitter space, is composed of three terms each of which alone represents a flat space. The existence of gradient CKV (GCKV) is examined in relation to vacuum and perfect fluid spacetimes.