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## Main Question or Discussion Point

I Have a problem understanding that vanishing of the curvature tensor implies that paralel transport is independent of path. With the converse of this assertion I have no problem.

The text I'm reading(Lovelock and Rund) explains the converse but treats the direct assertion as trivial. Can someone shed some light on this?

The text I'm reading(Lovelock and Rund) explains the converse but treats the direct assertion as trivial. Can someone shed some light on this?