Bach tensor

In differential geometry and general relativity, the Bach tensor is a tensor of rank 2 which is conformally invariant. In abstract indices the Bach tensor is given by

$B_{ab} = P_{dc}{{{C_a}^c}_b}^d+\nabla^c\nabla_aP_{bc}-\nabla^c\nabla_bP_{ac}$

where C is the Weyl tensor, and P the Schouten tensor given in terms of the Ricci tensor Ric and scalar curvature Sc by

$P_{ab}=\frac{1}{n-2}\left(\mathrm{Ric}_{ab}-\frac{\mathrm{Sc}}{2(n-1)}g_{ab}\right)$ .

This geometry-related article is a stub. You can help Wikipedia by expanding it.

This relativity-related article is a stub. You can help Wikipedia by expanding it.