Curvature tensor

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 the one of the numbers that are important in the Einstein field equations.