CONFORMAL EINSTEIN-SPACES

We study conformal transformations in four-dimensional manifolds. In particular, we present a new set of two necessary and sufficient conditions for a space to be conformal to an Einstein space. The first condition defines the class of spaces conformal to C spaces, whereas the last one (the vanishing of the Bach tensor) gives the particular subclass of C spaces which are conformally related to Einstein spaces. © 1985 Plenum Publishing Corporation