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Publications [#318264] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, R, Geodesically reversible Finsler 2spheres of constant curvature,
in Inspired by S. S. ChernA Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by Griffiths, PA, vol. 11
(Winter, 2006),
pp. 95111, World Scientific Publishers [math.DG/0407514]
(last updated on 2019/05/24)
Abstract: A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long standing problem in Finsler geometry.


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