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<p>In the setting of electromagnetic systems, we propose a new definition of electromagnetic Ricci curvature, naturally derived via the classical Jacobi–Maupertuis reparametrization from magnetic Ricci curvature [8,10]. On closed manifolds, we show that if the magnetic force is nowhere vanishing and the potential is sufficiently small in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm, then this Ricci curvature is positive for energies close to the maximum value of the potential <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(e_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>e</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. As a main application, under these assumptions, we extend the existence of contractible closed orbits at energy levels near <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(e_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>e</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> from <i>almost every</i> to <i>everywhere</i>.</p>

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Electromagnetic curvature via Jacobi–Maupertuis and beyond

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • V. Assenza,
  • G. Testolina

摘要

In the setting of electromagnetic systems, we propose a new definition of electromagnetic Ricci curvature, naturally derived via the classical Jacobi–Maupertuis reparametrization from magnetic Ricci curvature [8,10]. On closed manifolds, we show that if the magnetic force is nowhere vanishing and the potential is sufficiently small in the \(C^2\) C 2 norm, then this Ricci curvature is positive for energies close to the maximum value of the potential \(e_0\) e 0 . As a main application, under these assumptions, we extend the existence of contractible closed orbits at energy levels near \(e_0\) e 0 from almost every to everywhere.