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Publications [#243403] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, RL, Projectively flat Finsler 2spheres of constant curvature,
Selecta Mathematica, vol. 3 no. 2
(1997),
pp. 161203 [MR98i:53101], [dgga/9611010], [doi]
(last updated on 2018/12/18)
Author's Comments: This paper might be regarded as a sequel to the
previous one. In
it, I prove that, up to diffeomorphism, there is a
2parameter family of
Finsler metrics on the standard 2sphere whose
geodesics are the great
circles and whose FinslerGauss curvature is
identically 1. Explicit formulas
for these Finsler metrics are established and it is
shown that the only
symmetric Finsler metrics with this property are the
known Riemannian ones.
The introduction contains a discussion of the relation of
these results
with Hilbert's Fourth Problem.


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