Let suppose I have a Riemannian manifold and I define a connection on it. Is it true and safe to say that if a connection is torsionless and I parallel transport a vector along a loop made by geodesics I should have the same vector at the end of the loop?
Can anybody clarify this to me in plain english (I will translate in a formal way by myself). Thanks in advance.
Edit. I asked this question because I wanted to have a clearer picture about Torsion. So let's suppose for a while to have a Manifold with zero curvature. Is then safe to say that if the connection is torsionless when I make a loop along geodesics then the angle of the transported vector is the same as the original one?