Math @ Duke

Publications [#318264] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, RL, 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 2017/12/12)
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
longstanding problem in Finsler geometry.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

