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Riemann curvature tensor
In the
mathematical
field of
differential geometry
, the
Riemann curvature tensor
or
Riemann–Christoffel tensor
(after
Bernhard Riemann
and
Elwin Bruno Christoffel
) is the most common method used to express the
curvature of Riemannian manifolds
. It associates a
tensor
to each point of a
Riemannian manifold
(i.e., it is a
tensor field
), that measures the extent to which the
metric tensor
is not locally isometric to that of Euclidean space. The curvature tensor can also be defined for any
pseudo-Riemannian manifold
, or indeed any manifold equipped with an
affine connection
.
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