Geodesically reversible Finsler 2-spheres of constant curvature

Published

Book Section (Chapter)

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.

Full Text

Duke Authors

Cited Authors

  • Bryant, R

Cited Editors

  • Griffiths, PA

Published Date

  • 2006

Volume / Issue

  • 11 /

Book Title

  • Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician

Start / End Page

  • 95 - 111

Published By

Place of Publication

  • Hackensack, NJ