Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle

2012/10/25 by Zoltan Muzsnay, Muzsnay, Zoltan, Peter T. Nagy +1
Mathematics · #17B66 #22E65 #53B40 #53C29 #58D05 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:17B66 #msc:22E65 #msc:53B40 #msc:53C29 #msc:58D05

paper · pdf · doi:10.48550/arxiv.1210.6966

arxiv created 2012/10/25 · arxiv updated 2012/10/26

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.

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