Torsion
In elementary differential geometry in three dimensions, the torsion of a curve measures how sharply it is twisting. It is analogous to curvature in two dimensions. Given a vector-valued function r(t), the torsion at a given value of t is- ((r' × r")· r(3) ) ||r' × r"||-2.
where [u,v] is the Lie bracket of the two vector fields.
Torsion free connections are considered most frequently - the Levi-Civita connection is assumed to have zero torsion, for instance.
