I'm currently working through Do Carmo's book Riemannian Geometry and came across the following question:
Let $M$ be a Riemannian manifold with the following property: given any two points $p, q \in M$, the parallel transport from $p$ to $q$ does not depend on the curve that joins $p$ to $q$. Prove that the curvature of $M$ is identically zero, that is, for all $X, Y, Z \in \chi(M), R(X, Y)Z = 0$.
He gives most of the proof for us, and I'm able to fill in most of the details, but I don't know why the highlighted part below follows. I imagine it's something easy that I've just forgotten about.
