Projectively flat Finsler 2-spheres of constant curvature

Details Projectively flat Finsler 2-spheres of constant curvature Projectively flat Finsler 2-spheres of constant curvature

1996-11-25

arxiv.org/abs/dg-ga/9611010v1

Selecta Mathematica (N. S.) 3 (1997), 161-203

Mathematics

Differential Geometry

AMS-TeX v2.1, amsppt.sty (v. 2.1d), 38 pages

Scientific paper

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one. I discuss the history of the problem and its relation with Hilbert's Fourth Problem and the calculus of variations.

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