Conformally invariant Cotton and Bach tensor in N-dimensions

Abstract

This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a modification of the Cotton tensor, the other is a $n$--dimensional version of the Bach tensor. In general both tensors are smooth only on an open and dense subset of $M$, but this subset is invariant under conformal transformations. Moreover, we generalize the main result of "Conformal Einstein Spaces in $N$--Dimensions" published in \emph{Ann. Global Anal. Geom.} {\bf 20}(2) (2001).