Differential invariants for cubic integrals of geodesic flows on surfaces

作者：Matveev Vladimir S^*; Shevchishin Vsevolod V

来源：Journal of Geometry and Physics, 2010, 60(6-8): 833-856.

DOI：10.1016/j.geomphys.2010.02.002

• Polynomially integrable geodesic flows on surfaces
• Solvability of PDE
• Prolongation-projection method

We construct differential invariants that vanish if and only if the geodesic flow of a two-dimensional metric admits an integral of third degree in momenta with a given Birkhoff-Kolokoltsov 3-codifferential.

• 出版日期2010-8