 Riemann curvature tensor

The Riemann tensor measures the failure of covariant derivatives to commute.

The Riemann curvature tensor is a fundamental object in differential geometry and mathematical physics that measures the intrinsic curvature of a Riemannian manifold. It provides a way to describe how the geometry of a manifold is affected by its curvature. Specifically, it captures how much the geometry deviates from being flat, which corresponds to the geometry of Euclidean space.