Projectively flat Finsler 2-spheres of constant curvature

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

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Differential Geometry, 53C60 (Primary) 53A20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/152187

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9611010
 http://arxiv.org/abs/dg-ga/9611010
 Selecta Mathematica (N. S.) 3 (1997), 161-203

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arXiv