Beltrami's theorem


Beltrami's theorem

In mathematics — specifically, in Riemannian geometry — Beltrami's theorem is a result named after the Italian mathematician Eugenio Beltrami which states that geodesic maps preserve the property of having constant curvature. More precisely, if ("M", "g") and ("N", "h") are two Riemannian manifolds and "φ" : "M" → "N" is a geodesic map between them, and if either of the manifolds ("M", "g") or ("N", "h") has constant curvature, then so does the other one.

References

* cite book
last = Ambartzumian
first = R. V.
title = Combinatorial integral geometry
series = Wiley Series in Probability and Mathematical Statistics: Tracts on Probability and Statistics
publisher = John Wiley & Sons Inc.
location = New York
year = 1982
pages = p. 26
isbn = 0-471-27977-3
MathSciNet|id=679133
* cite book
last = Kreyszig
first = Erwin
title = Differential geometry
publisher = Dover Publications Inc.
location = New York
year = 1991
pages = pp. xiv+352
isbn = 0-486-66721-9
MathSciNet|id=1118149 (See section 91)

External links

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