This work investigates magnetic curves and flux surfaces in Euclidean 3-space, highlighting inflection points and their geometric properties.
We use the Bishop frame to investigate magnetic curves and magnetic vector fields in Euclidean 3-space, and address the case of magnetic curves with inflection points. Moreover, we study the differential geometric properties of magnetic flux surfaces, especially a special kind of magnetic flux surfaces (normal magnetic flux surfaces). We provide a physical explanation for the inflection points of the magnetic curves, which refer to the points where the charged particle experiences zero Lorentz force. These points also correspond to the singularities of the normal magnetic flux surfaces.
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Jiang et al. (2025) studied this question.
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