I recently watched Susskind video on general relativity. I am unsure why the commutator of the covariant derivative of the vectors is nonzero when there is curvature. E.g. DrDsVm-DsDrVm In flat space, that difference is zero. But why is it non zero in curved space? Someone please enlightened me! Sorry for being so vague as I don't really know how to express this in words and how to use this forum.