I'm trying to get a mental image of translation holonomy.
I start with rotational holonomy, which corresponds to intrinsic curvature. This is the quantitative failure of a continuous process of infinitesimal parallel transports using Levi-Civita connection along a closed curved, to return to the same orientation, as the length of the curve tends to 0.
Now, translation holonomy is said to be the quantitative failure of closing the curve, as the length tends to 0, And is the measure of torsion.
So, in the presence of torsion, using the Levi-Civita connection to parallel transport will land in a "wrong" tangent space. So can translation holonomy, torsion at a point, be calculated by using the Levi-Civita connection as in the rotational process, but measuring the vector of displacement from the initial point of the curve after finishing what was meant to be a closed curve, as the length of the curve tends to 0?