Bach tensor

The Bach tensor is a mathematical object in the field of differential geometry, specifically within the study of Riemannian and pseudo-Riemannian manifolds. It is a derived tensor that is associated with the Ricci curvature and the Weyl tensor, and it plays an important role in the classification of the geometric properties of manifolds. More precisely, the Bach tensor is defined in the context of four-dimensional Riemannian manifolds and is related to the conformal structure of the manifold.