2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143085In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Finally a correspondence of homogeneous geodesics to critical points of restricted Finsler metrics is given. Then results concerning the existence homogeneous geodesics are obtained.Differential Geometry53C60; 53C35; 53C30; 53C22text