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Contortion tensor - Wikipedia, the free encyclopedia

Contortion tensor

From Wikipedia, the free encyclopedia

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

The contortion tensor $K c a b$ is defined in terms of the torsion tensor $T c a b$ as

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

It is antisymmetric in the last two indices $K c a b = - K c b a$ , where $K c a b = g c d K d a b$ .

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