Weyl curvature tensor

This article defines a notion of curvature for a differential manifold equipped with a Riemannian metric

Definition

Loose definition

The Weyl curvature tensor for a Riemannian metric is a $(1,3)$-tensor that associates to each point the component of its Riemann curvature tensor that lies in the Weyl curvature space. Roughly speaking, it is what we get after subtracting the Ricci curvature tensor (multiplied by the identity matrix) from the Riemann curvature tensor.