TY - JOUR

T1 - On a Certain Sub-Riemannian Geodesic Flow on the Heisenberg Group

AU - Agapov, S. V.

AU - Borchashvili, M. R.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

KW - geodesic flow

KW - left-invariant metric

KW - sub-Riemannian geometry

UR - http://www.scopus.com/inward/record.url?scp=85042150619&partnerID=8YFLogxK

U2 - 10.1134/S0037446617060039

DO - 10.1134/S0037446617060039

M3 - Article

AN - SCOPUS:85042150619

VL - 58

SP - 943

EP - 951

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -