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)|
Torsion form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Torsion_form&oldid=18526