Contortion tensor

From Wikipedia, the free encyclopedia

Effect of torsion tensor on the Christoffel symbol and the spin connection.


The contortion tensor Kcab is defined in terms of the torsion tensor Tcab as

K^c{}_{ab}:= \frac{1}{2} (T^c{}_{ab} + T_{ab}{}^c + T_{ba}{}^c)


It is antisymmetric in the last two indices Kcab = − Kcba, where Kcab = gcdKdab.