Curvature tensor

From Encyclopedia of Mathematics
Revision as of 17:19, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A tensor of type obtained by decomposing the curvature form in a local co-basis on a manifold . In particular, in a holonomic co-basis , , the components of the curvature tensor of an affine connection are expressed in terms of the Christoffel symbols of the connection and their derivatives:

In similar fashion one defines the curvature tensor for an arbitrary connection on a principal fibre space with structure Lie group in terms of a decomposition of the appropriate curvature form; this applies, in particular, to conformal and projective connections. It takes values in the Lie algebra of the group and is an example of a so-called tensor with non-scalar components.

For references see Curvature.

How to Cite This Entry:
Curvature tensor. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article