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 Riemannian metrics which are invariant by such an action. In particular, we will be interested in the existence of geodesics which are closed up to the action of some element in the group $G$, since they project to closed magnetic geodesics on the quotient orbifold $Q/G$.

The proof of Theorem 1.5 in the previous version of the draft was erroneous. A weaker version of the aforementioned theorem is now stated and proved