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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2605.00483 |
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| _version_ | 1866910183547994112 |
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| author | Camacho, Misael Avendaño Mamani, Jhonny Kama Barreras, Eduardo Velasco |
| author_facet | Camacho, Misael Avendaño Mamani, Jhonny Kama Barreras, Eduardo Velasco |
| contents | We study the existence of Hamiltonian semisprays on Lie algebroids. This work is motivated by a problem studied by Vaisman for tangent bundles, and we extend this question to the setting of arbitrary Lie algebroids and provide a general solution.
More precisely, given a Lie algebroid and a regular Lagrangian, we construct a family of Poisson brackets on the algebroid such that the Hamiltonian vector field associated with the corresponding energy function is a semispray. Our approach is based on the symplectic geometry of the prolongation of a Lie algebroid and a cohomological analysis of its vertical subbundle. The results provide a geometric framework for second-order Hamiltonian dynamics on Lie algebroids, extending some known facts in the classical tangent bundle case and revealing new interactions between Poisson geometry and algebroid structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00483 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian semisprays on Lie algebroids Camacho, Misael Avendaño Mamani, Jhonny Kama Barreras, Eduardo Velasco Differential Geometry 53D17 (Primary), 53D05 (Secondary) We study the existence of Hamiltonian semisprays on Lie algebroids. This work is motivated by a problem studied by Vaisman for tangent bundles, and we extend this question to the setting of arbitrary Lie algebroids and provide a general solution. More precisely, given a Lie algebroid and a regular Lagrangian, we construct a family of Poisson brackets on the algebroid such that the Hamiltonian vector field associated with the corresponding energy function is a semispray. Our approach is based on the symplectic geometry of the prolongation of a Lie algebroid and a cohomological analysis of its vertical subbundle. The results provide a geometric framework for second-order Hamiltonian dynamics on Lie algebroids, extending some known facts in the classical tangent bundle case and revealing new interactions between Poisson geometry and algebroid structures. |
| title | Hamiltonian semisprays on Lie algebroids |
| topic | Differential Geometry 53D17 (Primary), 53D05 (Secondary) |
| url | https://arxiv.org/abs/2605.00483 |