In differential geometry, the term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold — see also Curvature of Riemannian manifolds; the curvature of an affine connection or covariant derivative (on tensors); the curvature form of an Ehresmann connection: see Ehresmann connection, connection (principal bundle) or connection (vector bundle). It is one of the numbers that are important in the Einstein field equations.
See also Tensor (disambiguation)