The holonomy of spherically symmetric projective Finsler metrics of constant curvature

2024/05/13 by Asma Mezrag, Mezrag, Asma, Zoltán Muzsnay +1
Physics and Astronomy · #22E65 #53B40 #53C29 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.07563

openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the holonomy group of n-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it is isomorphic to Diff_o(\mathbb S^n-1), the connected component of the identity of the group of smooth diffeomorphism on the (n-1)-dimensional sphere. In particular, the holonomy group of the n-dimensional standard Funk metric and the Bryant-Shen metrics are maximal and isomorphic to Diff_o(\mathbb S^n-1). These results are the firsts describing explicitly the holonomy group of n-dimensional Finsler manifolds in the non-Berwaldian (that is when the canonical connection is non-linear) case.

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