Geodesically reversible Finsler 2-spheres of constant curvature

Details Geodesically reversible Finsler 2-spheres of constant curvature Geodesically reversible Finsler 2-spheres of constant curvature

2004-07-29

arxiv.org/abs/math/0407514v2

Inspired by S. S. Chern--A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by P. A. Gr

Mathematics

Differential Geometry

11 pages, references added, some arguments improved and exposition rearranged

Scientific paper

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 2-sphere 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 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long-standing problem in Finsler geometry.

Affiliated with

Also associated with

No associations

Rating

Geodesically reversible Finsler 2-spheres of constant curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geodesically reversible Finsler 2-spheres of constant curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesically reversible Finsler 2-spheres of constant curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457548