On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

Abstract

Let $Q$ be a closed manifold admitting a locally free action of a compact Lie group $G$. In this paper, we study the properties of geodesic flows on $Q$ given by suitable G-invariant Riemannian metrics. In particular, we will be interested in the existence of geodesics that are closed up to the action of some element in the group $G$, since they project to closed magnetic geodesics on the quotient orbifold $Q/G$.