Beltrami's Theorem

Let f:M->N be a geodesic mapping. If either M or N has constant curvature, then both surfaces have constant curvature (Ambartzumian 1982, p. 26; Kreyszig 1991).

See also

Geodesic Mapping

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Ambartzumian, R. V. Combinatorial Integral Geometry. Chichester, England: Wiley, 1982.Kreyszig, E. §91 in Differential Geometry. New York: Dover, 1991.

Referenced on Wolfram|Alpha

Beltrami's Theorem

Cite this as:

Weisstein, Eric W. "Beltrami's Theorem." From MathWorld--A Wolfram Web Resource.

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