 Schouten tensor

For dimension $n\ge 3$, the Schouten tensor packages the Ricci tensor and scalar curvature in the trace part of the Riemann curvature tensor. In dimension three it is $S_{ij}=R_{ij}-R{g}_{ij}/4$, and the full Riemann curvature tensor is reconstructed from it.

The Schouten tensor is a mathematical object used in differential geometry and the theory of general relativity. It is a specific type of symmetric tensor derived from the Ricci curvature of a Riemannian or pseudo-Riemannian manifold.