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Projectively flat Finsler 2-spheres of constant curvature

Robert L. Bryant
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Abstract

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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BibTeXRIS

Robert L. Bryant. 1996-11-25. Projectively flat Finsler 2-spheres of constant curvature. https://arxiv.org/abs/dg-ga/9611010

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