Electromagnetic curvature via Jacobi-Maupertuis and beyond
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918180453089280 |
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| author | Assenza, Valerio Testolina, Giorgia |
| author_facet | Assenza, Valerio Testolina, Giorgia |
| contents | In the setting of electromagnetic systems, we propose a new definition of electromagnetic Ricci curvature, naturally derived via the classical Jacobi-Maupertuis reparametrization from the recent works of Assenza [IMRN, 2024] and Assenza, Marshall Reber, Terek [Communications in Mathematical Physics, 2025]. On closed manifolds, we show that if the magnetic force is nowhere vanishing and the potential is sufficiently small in the $C^2$ norm, then this Ricci curvature is positive for energies close to the maximum value of the potential $e_0$. As a main application, under these assumptions, we extend the existence of contractible closed orbits at energy levels near $e_0$ from almost every to everywhere. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_27514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electromagnetic curvature via Jacobi-Maupertuis and beyond Assenza, Valerio Testolina, Giorgia Differential Geometry Dynamical Systems Symplectic Geometry In the setting of electromagnetic systems, we propose a new definition of electromagnetic Ricci curvature, naturally derived via the classical Jacobi-Maupertuis reparametrization from the recent works of Assenza [IMRN, 2024] and Assenza, Marshall Reber, Terek [Communications in Mathematical Physics, 2025]. On closed manifolds, we show that if the magnetic force is nowhere vanishing and the potential is sufficiently small in the $C^2$ norm, then this Ricci curvature is positive for energies close to the maximum value of the potential $e_0$. As a main application, under these assumptions, we extend the existence of contractible closed orbits at energy levels near $e_0$ from almost every to everywhere. |
| title | Electromagnetic curvature via Jacobi-Maupertuis and beyond |
| topic | Differential Geometry Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2510.27514 |