Almost all Finsler metrics have infinite dimensional holonomy group

TL;DR

This paper proves that within the space of all Finsler metrics on a manifold, most have infinite-dimensional holonomy groups, indicating a prevalent complexity in their geometric structure.

Contribution

It demonstrates that the set of Finsler metrics with infinite-dimensional holonomy groups is open and dense, revealing the generic nature of this property.

Findings

Most Finsler metrics have infinite-dimensional holonomy groups.

The set of such metrics is open and dense in the space of all Finsler metrics.

Infinite-dimensional holonomy groups are a common feature in Finsler geometry.

Abstract

We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.