English

On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

Dynamical Systems 2017-11-29 v2 Differential Geometry Symplectic Geometry

Abstract

Let QQ be a closed manifold admitting a locally-free action of a compact Lie group GG. In this paper we study the properties of geodesic flows on QQ 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 GG, since they project to closed magnetic geodesics on the quotient orbifold Q/GQ/G.

Keywords

Cite

@article{arxiv.1711.07755,
  title  = {On geodesic flows with symmetries and closed magnetic geodesics on orbifolds},
  author = {Luca Asselle and Felix Schmäschke},
  journal= {arXiv preprint arXiv:1711.07755},
  year   = {2017}
}

Comments

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