Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle
Differential Geometry
2012-10-26 v1
Abstract
In this paper we show that the topological closure of the holonomy group of a certain class of projectively flat Finsler 2-manifolds of constant curvature is maximal, that is isomorphic to the connected component of the diffeomorphism group of the circle. This class of 2-manifolds contains the standard Funk plane of constant negative curvature and the Bryant-Shen-spheres of constant positive curvature. The result provides the first examples describing completely infinite dimensional Finslerian holonomy structures.
Keywords
Cite
@article{arxiv.1210.6966,
title = {Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle},
author = {Zoltan Muzsnay and Peter T. Nagy},
journal= {arXiv preprint arXiv:1210.6966},
year = {2012}
}