1996/11/25 by Robert L. Bryant · 1 citation
Mathematics · #dg-ga #math.DG #msc:53C60 #msc:53A20
published as Selecta Mathematica (N. S.) 3 (1997), 161-203 · AMS-TeX v2.1, amsppt.sty (v. 2.1d), 38 pages
arxiv created 1996/11/25 · arxiv updated 2009/11/30
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.