Periodic magnetic curves in elliptic Sasakian space forms

TL;DR

This paper studies periodic magnetic curves in elliptic Sasakian space forms, establishing conditions for their periodicity and a quantization principle for flowlines on Berger spheres, with specific criteria for the unit sphere.

Contribution

It introduces a new criterion for the periodicity of magnetic curves on the unit sphere and a quantization principle for flowlines in elliptic Sasakian space forms.

Findings

Established a criterion for periodic magnetic curves on ${ m S}^3$

Derived a quantization principle for flowlines on Berger spheres

Provided conditions for the existence of periodic solutions in these geometric settings

Abstract

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere ${\mathbb{S}}^3$.