From Wikipedia, the free encyclopedia
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
[edit]Topics referred to by the same term
This disambiguation page lists mathematics articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url