Torsion tensor
From Encyclopedia of Mathematics
A tensor of type that is skew-symmetric with respect to its indices, obtained by decomposing the torsion form of a connection in terms of a local cobasis on a manifold
. In particular, in terms of a holonomic cobasis
,
, the components
of the torsion tensor are expressed in terms of the Christoffel symbols (cf. Christoffel symbol)
of the connection as follows:
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Comments
In terms of covariant derivatives and vector fields
,
the torsion tensor
can be described as follows:
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References
[a1] | N.J. Hicks, "Notes on differential geometry" , v. Nostrand (1965) |
[a2] | D. Gromoll, W. Klingenberg, W. Meyer, "Riemannsche Geometrie im Grossen" , Springer (1968) |
[a3] | W. Klingenberg, "Riemannian geometry" , de Gruyter (1982) (Translated from German) |
How to Cite This Entry:
Torsion tensor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Torsion_tensor&oldid=49000
Torsion tensor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Torsion_tensor&oldid=49000
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article