# Weyl curvature tensor

From Diffgeom

*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 -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.