I'm in a logical loop here:(adsbygoogle = window.adsbygoogle || []).push({});

1. A tensor undergoesparallel transportif, as it moves through a manifold, its covariant derivative is zero.

2.Covariant derivativedescribes how a tensor changes as it moves through a manifold.

3. A tensor undergoeschangeas it moves if it does not parallel transport.

So how do I get out of this loop? I have an intuitive sense of parallel transport, but I do not know how to describe it mathematically except by using the definition above (1). Perhaps the answer lies in the calculus of variations?

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# How do I mathematically describe parallel transport?

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