FOUR-DIMENSIONAL CONFORMAL C-SPACES

Abstract

We investigate the structure of conformal C-spaces, a class of Riemannian manifolds which naturally arises as a conformal generalization of the Einstein condition. A basic question is when such a structure is closed, or equivalently locally conformally Cotton. In dimension four, we obtain a full answer to this question and also investigate the incidence of the Bach condition on this class of metrics. This is related to earlier results obtained in the Einstein–Weyl context.