Schouten tensor

In Riemannian geometry, the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten. It is defined for by:
where Ric is the Ricci tensor (defined by contracting the first and third indices of the Riemann tensor), "R" is the scalar curvature, "g" is the Riemannian metric, formula_2 is the trace of "P" and "n" is the dimension of the manifold.
The Weyl tensor equals the Riemann curvature tensor minus the Kulkarni–Nomizu product of the Schouten tensor with the metric. In an index notation
The Schouten tensor often appears in conformal geometry because of its relatively simple conformal transformation law
where formula_5