Bach tensor
In differential geometry and general relativity, the Bach tensor is a trace-free tensor of rank 2 which is conformally invariant in dimension. Before 1968, it was the only known conformally invariant tensor that is algebraically independent of the Weyl tensor. In abstract indices the Bach tensor is given by
where ' is the Weyl tensor, and ' the Schouten tensor given in terms of the Ricci tensor ' and scalar curvature ' by
