- 9,496

- 800

My thinking is that the metric gives the symmetric part of the Christoffel symbols of the second kind, but in the presence of torsion, there is also an asymmetric part for these symbols which is given by the torsion. However, I could use a sanity check here.

A related question: if we define a geodesic by saying that it parallel transports its own tangent vector, is the geodesic equation unaffected by the presence of the torsion? So the metric still gives us the geodesic equation, the unspecified torsion terms don't matter?