Contact line bundles, foliations, and integrability
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913889849966592 |
|---|---|
| author | Jovanovic, Bozidar |
| author_facet | Jovanovic, Bozidar |
| contents | We formulate the non-commutative integrability of contact systems on a contact manifold $(M,\mathcal H)$ using the Jacobi structure on the space of sections $Γ(L)$ of a contact line bundle $L$. In the cooriented case, if the line bundle is trivial and $\mathcal H$ is the kernel of a globally defined contact form $α$, the Jacobi structure on the space of sections reduces to the standard Jacobi structure on $(M,α)$. We therefore treat contact systems on cooriented and non-cooriented contact manifolds simultaneously. In particular, this allows us to work with dissipative Hamiltonian systems where the Hamiltonian does not have to be preserved by the Reeb vector field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact line bundles, foliations, and integrability Jovanovic, Bozidar Symplectic Geometry Exactly Solvable and Integrable Systems 37J35, 37J55, 53D10, 53C12 We formulate the non-commutative integrability of contact systems on a contact manifold $(M,\mathcal H)$ using the Jacobi structure on the space of sections $Γ(L)$ of a contact line bundle $L$. In the cooriented case, if the line bundle is trivial and $\mathcal H$ is the kernel of a globally defined contact form $α$, the Jacobi structure on the space of sections reduces to the standard Jacobi structure on $(M,α)$. We therefore treat contact systems on cooriented and non-cooriented contact manifolds simultaneously. In particular, this allows us to work with dissipative Hamiltonian systems where the Hamiltonian does not have to be preserved by the Reeb vector field. |
| title | Contact line bundles, foliations, and integrability |
| topic | Symplectic Geometry Exactly Solvable and Integrable Systems 37J35, 37J55, 53D10, 53C12 |
| url | https://arxiv.org/abs/2502.02935 |