Integrability of the sub-Riemannian geodesic flow of the left-invariant metric on the Heisenberg group

In this paper, we study two different classes of normal geodesic flows corresponding to the left-invariant sub-Riemannian metric on the \((2n+1)\)-dimensional Heisenberg group. The first class corresponds to the left-invariant distribution, while the second corresponds to the right-invariant one. We...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Pavlovic, Milan, Sukilovic, Tijana
Format: Article
Language:English
Subjects:
Invariants
Online Access:Get full text
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Summary:In this paper, we study two different classes of normal geodesic flows corresponding to the left-invariant sub-Riemannian metric on the \((2n+1)\)-dimensional Heisenberg group. The first class corresponds to the left-invariant distribution, while the second corresponds to the right-invariant one. We prove that corresponding Hamiltonian L-L and L-R systems are completely integrable.
ISSN:2331-8422