Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie   Groups
  Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liouville integrability and superintegrability are proved. 
Alexey P. Mashtakov, Yuri L. Sachkov
math.OC