# Changes

## Torsion is tensorial

, 17:56, 6 January 2012
Statement
Then, $\tau(\nabla)$ is a [[fact about::tensorial map]] in both coordinates. In other words, the value of $\tau(\nabla)$ at a point $p \in M$ depends only on $\nabla, X(p), Y(p)$ and does not depend on the values of the vectors fields $X,Y$ at points other than $p$.

More explicitly, for any point $p \in M$, $\tau(\nabla)$ defines a bilinear map:

$\! \tau(\nabla): T_p(M) \times T_p(M) \to T_p(M)$

Further, since in fact [[torsion is antisymmetric]], this is an alternating bilinear map.
==Related facts==