Assuming that we are working with an infinitessimally small region of a manifold so that we can consider only first order effects, does parallel transport in the absence of torsion necessarily "close the quadrilateral"? What I mean is, if I have two vectors (very small vectors) V and U, and I parallel transported V along U, and vice versa, will the resulting 4 vectors (2 original, 2 parallel transported) form a closed quadrilateral?(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to get an intuition for torsion, and it seems to me that torsion would be the quantity which prevented the closing of the quadrilateral. I just wanted to confirm this, it seems right to me, but I can't be sure.

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# Parallel transport

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