This expresses the
naturality of the exponential map on a Riemannian
manifold. It boils down to the fact that an isometry
(distance-preserving map) between two Riemannian manifolds takes
geodesics to geodesics.
REFERENCE:
John M. Lee, Riemannian
Manifolds: An Introduction to Curvature, New York,
Springer-Verlag, 1997, page 76.
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