Generic existence of infinitely many non-contractible closed geodesics on compact space forms (Q6596309)

In this paper the authors study the problem of the existence of infinitely many geometrically distinct closed geodesics on a compact Riemannian manifold, or more generally Finsler manifold. This is one of the most important problem in Differerential Geometry and several contributes have been by many authors as W. Klingenberg, D. Gromoll and W. Meyer, A. Katok, J. Franks, V. Bangert, Y. Long.\N\NIn the paper under review the authors prove that there are infinitely many noncontractible closed geodesics of class \([h]\) on a compact space form with \(C^r\)-generic Finsler metrics, with \(4 \leq r \leq \infty\). If the metric is Riemannian, the same conclusion holds for \(2 \leq r \leq \infty\). The proof is based on the resonance identity of non-contractible closed geodesics on space forms.