Contorsion tensor

From Wikipedia, the free encyclopedia

The contorsion tensor in differential geometry expresses the effect of the torsion tensor on the Christoffel symbol and the spin connection.

The contorsion tensor K^c_ab is defined in terms of the torsion tensor T^c_ab as follows:

The contorsion tensor is antisymmetric in the last two indices:

K_cab = − K_cba,

where

K_cab = g_cdK^d_ab.