On Magnetic Curves with Fermi-Walker Derivative in Double Isotropic Space

Abstract

Magnetic curves play an important role in mathematical physics, as they model the trajectories of charged particles subjected to a magnetic field F on a Riemannian manifold. The corresponding motion is governed by the Lorentz force ∅. Physically, the magnetic field influences the particle throughout its motion, causing it to follow a magnetic trajectory instead of a geodesic. In this study, we first compute the Fermi–Walker derivatives of Lorentz forces within the framework of equiform differential geometry in double isotropic space. We subsequently determine the formula associated with the Fermi–Walker derivatives of magnetic curves in this space. Finally, we establish several new results concerning the energy relationships of certain vector fields derived from this novel approach.

Keywords

• Isotropic space
• Magnetic curves
• Fermi-Walker derivative

Ethical Statement

Ethics committee approval was not required for this study because of there was no study on animals or humans.

Thanks

This article is derived from the author's unpublished doctoral dissertation.

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