# Difference between revisions of "Torsion tensor"

A tensor of type \$ ( 1, 2) \$ that is skew-symmetric with respect to its indices, obtained by decomposing the torsion form of a connection in terms of a local cobasis on a manifold \$ M ^ {n} \$. In particular, in terms of a holonomic cobasis \$ dx ^ {i} \$, \$ i = 1 \dots n \$, the components \$ S _ {ij} ^ {k} \$ of the torsion tensor are expressed in terms of the Christoffel symbols (cf. Christoffel symbol) \$ \Gamma _ {ij} ^ {k} \$ of the connection as follows:

\$\$ S _ {ij} ^ {k} = \Gamma _ {ij} ^ {k} - \Gamma _ {ji} ^ {k} . \$\$