The geometry of electromagnetic curves on Riemannian manifolds

TL;DR

This paper defines electromagnetic curves on Riemannian manifolds and explores the specific case of a charged particle moving on a sphere in a magnetic field, linking geometric concepts with physical motion.

Contribution

It introduces a clear definition of electromagnetic curves on Riemannian manifolds and applies it to a concrete example involving magnetic fields on a sphere.

Findings

Explicit description of a charged particle's motion on a sphere under magnetic influence

Connection between geometric electromagnetic curves and physical particle trajectories

Illustration of electromagnetic curves in a specific Riemannian setting

Abstract

We present a concise definition of an electromagnetic curve on a Riemannian manifold and illustrate the explicit case of the motion of a charged particle on the unit sphere under the influence of a uniform magnetic field.