The define of geodesic is in below picture which is from Wiki. I don't know why it is generalize of geodesic for Riemannian manifolds. In fact , I can't see it is the shortest when two point are enough near . Besides, the existence is not obvious, what make sure the existence of geodesic in metric space ?
2026-03-28 17:39:18.1774719558
Geodesic of metric space
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