Suppose you wanted to know the geodesic between two points in a manifold, where the points do not exist in the same chart. Would the fact that they are not in the same chart make a difference? How would you work out the components of the metric when they are dependent on locally defined tangent vectors but your curve exists in multiple coordinate charts?
2026-05-14 13:47:45.1778766465
Geodesics in Riemannian Manifolds
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