Homogeneity of magnetic trajectories in the Berger sphere

TL;DR

This paper investigates the properties of magnetic trajectories in Berger spheres, showing that they can be decomposed into a homogeneous geodesic and a charged Reeb flow, highlighting their structured nature.

Contribution

It establishes that contact magnetic trajectories in Berger spheres are composed of a homogeneous geodesic and a charged Reeb flow, revealing their homogeneous structure.

Findings

Contact magnetic trajectories are products of homogeneous geodesics and charged Reeb flows.

Homogeneity of magnetic trajectories in Berger spheres is characterized.

The structure of trajectories depends on the Reeb flow and geodesic properties.

Abstract

We study the homogeneity of contact magnetic trajectories in naturally reductive Berger spheres. We prove that every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.