Torsion form

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The covariant differential of the vector-valued -form of the displacement of an affine connection, the -form

where is the connection form. The torsion form satisfies the first Bianchi identity:

where is the curvature form of the given connection. The definition of a torsion form for reductive connections is analogous.



[a1] S. Kobayashi, K. Nomizu, "Foundations of differential geometry" , 1–2 , Interscience (1963)
How to Cite This Entry:
Torsion form. 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