Geometrical Obstruction to the Integrability of Geodesic Flows: an   Application to the Anisotropic Kepler Problem
  Resorting to classical techniques of Riemannian geometry we develop a geometrical method suitable to investigate the nonintegrability of geodesic flows and of natural Hamiltonian systems. Then we apply such method to the Anisotropic Kepler Problem (AKP) and we prove that it is not analytically integrable. 
Manuele Santoprete