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arXiv · 2510.27514

Electromagnetic curvature via Jacobi-Maupertuis and beyond

Valerio Assenza·Giorgia Testolina
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Abstract

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.

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Valerio Assenza, Giorgia Testolina. 2025-10-31. Electromagnetic curvature via Jacobi-Maupertuis and beyond. https://doi.org/10.1007/s11784-026-01314-7

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