field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...

Like the Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from...

the Ricci tensor contains all of the information which in higher dimensions is encoded by the more complicated Riemann curvature tensor. In part, this...

given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions...

the full Riemann curvature tensor. Alternatively, in a coordinate-free notation one may use Riem for the Riemann tensor, Ric for the Ricci tensor and R for...

(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tensor, curvature tensor, ...), and...

differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry can...

A a tensor field on M. Many mathematical structures called "tensors" are also tensor fields. For example, the Riemann curvature tensor is a tensor field...

metric (and the associated curvature tensors) to the stress–energy tensor T μ ν {\displaystyle T_{\mu \nu }} . This tensor equation is a complicated set...

way of measuring the curvature of a manifold is with an object called the Riemann (curvature) tensor. This tensor measures curvature by use of an affine...