There's a close relationship between curvature and the holonomy group; the holonomy theorem of Ambrose and Singer, for example. It seems to me that there should be an analogous result for torsion. I ...
I am asking this in the context of differential geometry (specifically Riemannian). When the Levi-Civita Connection is defined, we require that the torsion tensor is 0, which in local coordinates ...