A geodesic mapping 
between two Riemannian manifolds is a diffeomorphism
sending geodesics of 
into geodesics of 
, whose inverse also sends geodesics
to geodesics (Ambartzumian 1982, p. 26).
Geodesic Mapping
See also
Beltrami's Theorem, GeodesicExplore with Wolfram|Alpha
References
Ambartzumian, R. V. Combinatorial Integral Geometry. Chichester, England: Wiley, 1982.Kreyszig, E. Differential Geometry. New York: Dover, 1991.Referenced on Wolfram|Alpha
Geodesic MappingCite this as:
Weisstein, Eric W. "Geodesic Mapping." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeodesicMapping.html