Magnetic flux surfaces and magnetic curves with Bishop frame in Euclidean 3-space

2025/09/30 by Xiaoyan Jiang, Boyuan Xu, B. Xu +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Earth and Planetary Sciences · #Geomagnetism and Paleomagnetism Studies #Black Holes and Theoretical Physics #Geophysics and Gravity Measurements

paper · doi:10.1142/s0217732325501809

Abstract

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.

Citations

• Magnetic curves corresponding to Killing magnetic fields in \mathbb E³E3
• Magnetic vortex filament flows
• A new approach for magnetic curves in 3D Riemannian manifolds

Related

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• Geometric properties of lightlike magnetic curves and magnetic flux surfaces in Minkowski 3-space
• Magnetic curves corresponding to Killing magnetic fields in \mathbb E³E3
• Dual magnetic curves and flux ruled surfaces
• Magnetic spherical indicatrix of a ruled surface