# Changes

## Torsion of a linear connection

, 17:46, 6 January 2012
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A linear connection whose torsion is zero is termed a '''torsion-free linear connection'''.

==Facts==
===Tensoriality===
{{further|[[Torsion is tensorial]]}}
The torsion map is a $(1,2)$ tensor. It is tensorial in both $X$ and $Y$. This means that the value of the torsion of a connection for two vector fields at a point depends only on the values of the vector fields at that point. In other words, $\tau(\nabla)(X,Y)$ at $p$ depends on $\nabla, X(p), Y(p)$ only and does not depend on how $X$ and $Y$ behave elsewhere on the manifold.