Projectively flat Finsler manifolds with infinite dimensional holonomy

2012/02/05 by Zoltan Muzsnay, Muzsnay, Zoltan, Peter T. Nagy +1
Mathematics · #22E65 #53B40 #53C29 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E65 #msc:53B40 #msc:53C29

paper · pdf · doi:10.48550/arxiv.1202.0982

15 pages

arxiv created 2012/02/05 · arxiv updated 2012/02/07

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.

Related

• Characterization of projectively flat Finsler manifolds of constant curvature with finite dimensional holonomy group
• The holonomy group of projectively flat Randers two-manifolds of constant curvature
• Finsler manifolds with non-Riemannian holonomy
• Finsler spaces with infinite dimensional holonomy group
• Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle