On a Certain Sub-Riemannian Geodesic Flow on the Heisenberg Group
- Authors: Agapov S.V.1, Borchashvili M.R.2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 58, No 6 (2017)
- Pages: 943-951
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171538
- DOI: https://doi.org/10.1134/S0037446617060039
- ID: 171538
Cite item
Abstract
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.
About the authors
S. V. Agapov
Sobolev Institute of Mathematics
Author for correspondence.
Email: agapov@math.nsc.ru
Russian Federation, Novosibirsk
M. R. Borchashvili
Novosibirsk State University
Email: agapov@math.nsc.ru
Russian Federation, Novosibirsk