Magnetic equations on the Heisenberg group: symmetries, solutions and the inverse problem of the calculus of variations
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910031964798976 |
|---|---|
| author | Ovando, Gabriela Subils, Mauro |
| author_facet | Ovando, Gabriela Subils, Mauro |
| contents | The Heisenberg Lie group $H_3$ is modeled on the differentiable structure of $\mathbb{R}^3$ but equipped with another non-commutative product operation. By fixing the usual metric on the Heisenberg Lie group, this work provides a comprehensive overview of the behavior of magnetic geodesics for any invariant Lorentz force. After writing the magnetic equations, we found symmetries that enable the explicit computation of the magnetic trajectories for any homogeneous exact and non-exact magnetic form. Finally we show that these magnetic trajectories are solutions of a variational problem: we present explicit examples of Lagrangians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magnetic equations on the Heisenberg group: symmetries, solutions and the inverse problem of the calculus of variations Ovando, Gabriela Subils, Mauro Differential Geometry 53C99, 70G65, 70F17, 22E25 The Heisenberg Lie group $H_3$ is modeled on the differentiable structure of $\mathbb{R}^3$ but equipped with another non-commutative product operation. By fixing the usual metric on the Heisenberg Lie group, this work provides a comprehensive overview of the behavior of magnetic geodesics for any invariant Lorentz force. After writing the magnetic equations, we found symmetries that enable the explicit computation of the magnetic trajectories for any homogeneous exact and non-exact magnetic form. Finally we show that these magnetic trajectories are solutions of a variational problem: we present explicit examples of Lagrangians. |
| title | Magnetic equations on the Heisenberg group: symmetries, solutions and the inverse problem of the calculus of variations |
| topic | Differential Geometry 53C99, 70G65, 70F17, 22E25 |
| url | https://arxiv.org/abs/2602.21187 |