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arXiv · 1202.0982

Projectively flat Finsler manifolds with infinite dimensional holonomy

Zoltan Muzsnay·Peter T. Nagy
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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 $> 2$ 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.

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Zoltan Muzsnay, Peter T. Nagy. 2012-02-05. Projectively flat Finsler manifolds with infinite dimensional holonomy. https://arxiv.org/abs/1202.0982

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