Geodesic distance refers to the shortest path between two points on a given surface or manifold, which is measured along the surface itself. This concept is fundamental in differential geometry as it relates to geodesics, which are curves that locally minimize distance. Understanding geodesic distance allows for insights into the curvature and structure of spaces, connecting various important concepts like the exponential map, minimizing properties of curves, geodesic equations, and results such as the Bonnet-Myers theorem.
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