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Paper

Classification of the geodesic curves of the sub-Riemannian LR system on the Heisenberg group in dimension 5

Abstract

We study the geodesic flow corresponding to the left-invariant sub-Riemannian metric and the right-invariant distribution on the second Heisenberg group. The corresponding Hamiltonian system is completely integrable and in this paper we study its solutions. We obtain a complete classification of the geodesic curves. Moreover, we compute as the first step of the quadrature.