On Integrability of Certain Rank 2 Sub-Riemannian Structures

    2017, Volume 22, Number 5, pp.  502-519

    Author(s): Kruglikov B., Vollmer A., Lukes-Gerakopoulols G.

    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.
    Keywords: Sub-Riemannian geodesic flow, Killing tensor, integral, symmetry, Tanaka prolongation, overdetermined system of PDE, prolongation
    Citation: Kruglikov B., Vollmer A., Lukes-Gerakopoulols G., On Integrability of Certain Rank 2 Sub-Riemannian Structures, Regular and Chaotic Dynamics, 2017, Volume 22, Number 5, pp. 502-519

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