- Beltrami's theorem
In

mathematics — specifically, inRiemannian geometry —**Beltrami's theorem**is a result named after the Italianmathematician Eugenio Beltrami which states thatgeodesic map s preserve the property of havingconstant curvature . More precisely, if ("M", "g") and ("N", "h") are twoRiemannian 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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