Projectively flat Finsler manifolds with infinite dimensional holonomy
Differential Geometry
2012-02-07 v1
Abstract
Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group can not be a compact Lie group, if the Finsler manifold of dimension has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holonomy properties of projectively flat Finsler manifolds of non-zero constant flag curvature. We prove in particular that projectively flat Randers and Bryant-Shen manifolds of non-zero constant flag curvature have infinite dimensional holonomy group.
Keywords
Cite
@article{arxiv.1202.0982,
title = {Projectively flat Finsler manifolds with infinite dimensional holonomy},
author = {Zoltan Muzsnay and Peter T. Nagy},
journal= {arXiv preprint arXiv:1202.0982},
year = {2012}
}
Comments
15 pages