The curvature of left-invariant magnetic systems

Shane Rankin; Ivo Terek; David Weed

The curvature of left-invariant magnetic systems

Differential Geometry 2026-07-10 v1

Authors: Shane Rankin , Ivo Terek , David Weed

Abstract

We compute the magnetic curvatures (in the sense of Assenza) of left-invariant magnetic systems on Lie groups and explore relations between curvature properties and algebraic properties, extending to the magnetic setting a number of results from Milnor's classic 1976 paper on the geometry of left-invariant metrics. We also discuss the existence of non-trivial bi-invariant magnetic systems and exhibit the resulting curvature formulas in some concrete examples, including the Heisenberg group.

Keywords

magnetic curvature left-invariant metrics Lie groups bi-invariant magnetic systems Heisenberg group

Cite

@article{arxiv.2607.09107,
  title  = {The curvature of left-invariant magnetic systems},
  author = {Shane Rankin and Ivo Terek and David Weed},
  journal= {arXiv preprint arXiv:2607.09107},
  year   = {2026}
}

Comments

19 pages, 1 figure