The C-connection and the 4-dimensional Einstein spaces

Abstract

We introduce a new family of operators in 4-dimensional pseudo-Riemannian manifolds with a non-vanishing Weyl scalar (non-degenerate spaces) that keep the conformal covariance of conformally covariant tensor concomitants. A particular case that arises naturally is the -connection that is a Weyl connection that keeps conformal invariance. Using the connection we give a new characterization of non-degenerate spaces that are conformal to an Einstein space.