For this very reason, it is commonly used to express the contribution that the Ricci curvature (or rather, the Schouten tensor) and the Weyl tensor each makes to the curvature of a Riemannian manifold.
This concept is used to demonstrate how the Ricci curvature (or the Schouten tensor) and the Weyl tensor contribute to the total curvature of a Riemannian manifold.