Classification of the geodesic curves of the sub-Riemannian LR system on the Heisenberg group in dimension 5
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913088026968064 |
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| author | Pavlović, Milan |
| author_facet | Pavlović, Milan |
| contents | 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 $r(t)$ as the first step of the quadrature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of the geodesic curves of the sub-Riemannian LR system on the Heisenberg group in dimension 5 Pavlović, Milan Differential Geometry 53C17, 22E25, 37J35 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 $r(t)$ as the first step of the quadrature. |
| title | Classification of the geodesic curves of the sub-Riemannian LR system on the Heisenberg group in dimension 5 |
| topic | Differential Geometry 53C17, 22E25, 37J35 |
| url | https://arxiv.org/abs/2512.11155 |