Differential geometry | Geodesic (mathematics)

Geodesic map

In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ−1 of any geodesic arc in N is a geodesic arc in M. (Wikipedia).

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Related pages

Inverse function | Identity function | Dimension | Geodesic | Mathematics | Differential geometry | Function (mathematics) | Homeomorphism | Gnomonic projection | Diffeomorphism | Hyperbolic geometry | Riemannian manifold | Isometry | Euclidean space | Pseudo-Riemannian manifold | Radius