On integrability of certain rank 2 sub-Riemannian structures |
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| Authors: | Boris S. Kruglikov Andreas Vollmer Georgios Lukes-Gerakopoulos |
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| Affiliation: | 1.Institute of Mathematics and Statistics,University of Troms?,Troms?,Norway;2.Mathematisches Institut,Friedrich-Schiller-Universit?t,Jena,Germany;3.INdAM - Politecnico di Torino, Dipartimento di Scienze Matematiche,Torino,Italy;4.Institute of Theoretical Physics, Faculty of Mathematics and Physics,Charles University in Prague,Prague,Czech Republic;5.Astronomical Institute of the Academy of Sciences of the Czech Republic,Prague,Czech Republic |
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| Abstract: | We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows. |
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