Homogeneity of magnetic geodesics in the Heisenberg group

TL;DR

This paper proves that magnetic geodesics in the 3D Heisenberg group, derived from its canonical contact structure, exhibit homogeneity, revealing a symmetric property of these curves.

Contribution

It establishes the homogeneity of magnetic geodesics in the Heisenberg group, a novel geometric property related to its contact structure.

Findings

Magnetic geodesics in the Heisenberg group are homogeneous.

The result links contact geometry with magnetic geodesic properties.

Homogeneity implies symmetric behavior of these geodesics.

Abstract

We prove that magnetic geodesics in the $3$-dimensional Heisenberg group derived from the canonical contact structure are homogeneous.