Main Question or Discussion Point
Many sources give explanations of the Riemann tensor that involve parallel transporting a vector around a loop and finding its deviation when it returns. They then show that this same tensor can be derived by taking the commutator of second covariant derivatives. Is there a way to understand why these two derivations are related? In other words, is there an intuitive way to get to the commutator definition of the Riemann tensor directly from the idea of parallel transport?