Projectively flat Finsler manifolds with infinite dimensional holonomy

Details Projectively flat Finsler manifolds with infinite dimensional holonomy Projectively flat Finsler manifolds with infinite dimensional holonomy

2012-02-05

arxiv.org/abs/1202.0982v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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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