On the Holonomy of Finsler Manifolds

Abstract

This thesis investigates the holonomy structure of Finsler manifolds, a natural gen- eralization of Riemannian geometry in which the notion of length depends on both position and direction. While holonomy theory is well understood in the Riemannian setting, its Finslerian counterpart exhibits fundamentally different and often more complex behavior, frequently leading to infinite-dimensional structures. The aim of this work is to deepen the understanding of these phenomena by analyzing maxi- mal holonomy, classifying holonomy groups in specific cases, and introducing new geometric frameworks related to navigation problems.