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Let M {\displaystyle M} and N {\displaystyle N} be Riemannian manifolds. A geodesic mapping from M {\displaystyle M} to N {\displaystyle N} is a diffeomorphism from M {\displaystyle M} to N {\displaystyle N} that sends geodesics to geodesics, such that its inverse also sends geodesics to geodesics.
