Projectively flat finsler 2-spheres of constant curvature

Published

Journal Article

After recalling the structure equations of Finsler structures on surfaces, I define a notion of "generalized Finsler structure" as a way of microlocalizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of "generalized path geometry" analogous to that of "generalized Finsler structure." I use these ideas to study the geometry of Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature K and whose geodesic path geometry is projectively flat, i.e., locally equivalent to that of straight lines in the plane. I show that, modulo diffeomorphism, there is a 2-parameter family of projectively flat Finsler structures on the sphere whose Finsler-Gauss curvature K is identically 1. © Birkhäuser Verlag, 1997.

Full Text

Duke Authors

Cited Authors

  • Bryant, RL

Published Date

  • January 1, 1997

Published In

Volume / Issue

  • 3 / 2

Start / End Page

  • 161 - 203

Electronic International Standard Serial Number (EISSN)

  • 1420-9020

International Standard Serial Number (ISSN)

  • 1022-1824

Digital Object Identifier (DOI)

  • 10.1007/s000290050009

Citation Source

  • Scopus