In Riemannian geometry the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten defined for n ≥ 3 by: P = 1 n − 2 ⇔ R i c = P + J g, {\displaystyle P={\frac {1}{n-2}}\left\,\Leftrightarrow \mathrm {Ric} =P+Jg\,,} where Ric is the Ricci tensor, R is the scalar curvature, g is the Riemannian metric, J = 1 2 R {\displaystyle J={\frac {1}{2}}R} is the trace of P and n is the dimension of the manifold. Wikipedia