23 nov 2021 -- 17:00
Geometry in Como - online
Abstract.
From the perspective of classical mechanics, a charged particle moving on a Riemannian manifold $M$ experiences a Lorentz force, and its trajectory is called a magnetic trajectory. The Lorentz force determines a magnetic field which is introduced as a closed 2-form on $M$. In this work, we focus on 2-step nilpotent Lie groups equipped with a left-invariant metric and a left-invariant magnetic field. The aim is to study magnetic fields, their corresponding magnetic equations and solutions. We obtain existence results regarding closed 2-forms and explicit expressions for a family of magnetic trajectories. Some ideas concerning closedness conditions are analysed.