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, R is the scalar curvature, g is the Riemannian metric, 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
