A Toponogov type triangle comparison theorem in Finsler geometry
Differential Geometry
2013-09-17 v2
Abstract
The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to the base point is contained in a Berwald-like region, and that the Finsler metric is convex enough in the radial directions in that region.
Cite
@article{arxiv.1205.3913,
title = {A Toponogov type triangle comparison theorem in Finsler geometry},
author = {Kei Kondo and Shin-ichi Ohta and Minoru Tanaka},
journal= {arXiv preprint arXiv:1205.3913},
year = {2013}
}
Comments
The version 2 was corrected as follows: we additionally assume G(\rho)\not= 0 in Theorem 1.2. And some other minor changes have been done in the version 2. 19 pages, no figures