Characterization of projectively flat Finsler manifolds of constant curvature with finite dimensional holonomy group

2013/04/05 by Zoltán Muzsnay, Zoltan Muzsnay, Péter T. Nagy +4
Mathematics · Physics and Astronomy · #17B66 #53B40 #53C29 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:17B66 #msc:53B40 #msc:53C29

paper · pdf · doi:10.48550/arxiv.1304.1813

9 pages

openalex publication_date 2013/04/05 · arxiv created 2013/04/12 · arxiv updated 2013/04/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian.

Related

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