Torsion of a linear connection
This article defines a tensor (viz a section on a tensor bundle over the manifold) of type (1,2)
The torsion of , denoted as , is defined as a map that takes as input 2 vector fields and outputs a third vector field, as follows:
A linear connection whose torsion is zero is termed a torsion-free linear connection.
Further information: Torsion is tensorial The torsion map is a tensor. It is tensorial in both and .