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<p>In this study, the geometry of magnetic curves and magnetic flux surfaces in Euclidean 3-space are investigated within a novel framework called the Conjugate Rotation Minimizing Frame (CRMF). Magnetic curves are described via the Lorentz force equation, and the associated Killing magnetic vector fields are obtained for each curve. Magnetic flux surfaces are generated by the motion of these Killing magnetic vector fields along the magnetic curves, and the developability conditions of the resulting surfaces are characterized in terms of the curvature functions and the geometric constraints imposed by the Killing field. In addition, the existence and nature of singular points on these surfaces are examined. Finally, to demonstrate the theoretical findings, explicit examples of magnetic curves with different curvature profiles and their corresponding magnetic flux surfaces are presented.</p>

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A Unified Approach to Magnetic Curves and Flux Surfaces via Conjugate Rotation Minimizing Frame

  • 期刊论文

  • 发表日期：

    2026年7月27日

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摘要

In this study, the geometry of magnetic curves and magnetic flux surfaces in Euclidean 3-space are investigated within a novel framework called the Conjugate Rotation Minimizing Frame (CRMF). Magnetic curves are described via the Lorentz force equation, and the associated Killing magnetic vector fields are obtained for each curve. Magnetic flux surfaces are generated by the motion of these Killing magnetic vector fields along the magnetic curves, and the developability conditions of the resulting surfaces are characterized in terms of the curvature functions and the geometric constraints imposed by the Killing field. In addition, the existence and nature of singular points on these surfaces are examined. Finally, to demonstrate the theoretical findings, explicit examples of magnetic curves with different curvature profiles and their corresponding magnetic flux surfaces are presented.