Siberian Mathematical Journal

, Volume 58, Issue 6, pp 943–951 | Cite as

On a Certain Sub-Riemannian Geodesic Flow on the Heisenberg Group



Under study is an integrable geodesic flow of a left-invariant sub-Riemannian metric for a right-invariant distribution on the Heisenberg group. We obtain the classification of the trajectories of this flow. There are a few examples of trajectories in the paper which correspond to various values of the first integrals. These trajectories are obtained by numerical integration of the Hamiltonian equations. It is shown that for some values of the first integrals we can obtain explicit formulae for geodesics by inverting the corresponding Legendre elliptic integrals.


sub-Riemannian geometry geodesic flow left-invariant metric 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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