Torsion of connection
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Torsion of affine connection 
is a (1,2) tensor given by the formula
![T(u,v)=\nabla_u v - \nabla_v u -[u,v]](../../../math/e/c/d/ecd4f1c662b1ca014d808a855e9bf3c8.png)
where [u,v] is the Lie bracket of the two vector fields.
A connection is torsion-free if its torsion tensor is identically zero. Torsion-free connections are considered most frequently - the Levi-Civita connection is assumed to have zero torsion, for instance.
