Magnetic Killing tensors and first integrals of the magnetic flow
Differential Geometry
2026-02-23 v1 Dynamical Systems
Abstract
In this work we introduce a new family of symmetric tensors generalizing Killing tensors, that we call magnetic Killing symmetric tensors. We make use of them to construct first integrals for the magnetic flow associated to a given magnetic field. We apply the results to prove integrability of some invariant magnetic flows (either exact or non-exact) on some 2-step nilmanifolds: the Kodaira-Thurston manifold and Heisenberg nilmanifolds of higher dimensions.
Cite
@article{arxiv.2602.18373,
title = {Magnetic Killing tensors and first integrals of the magnetic flow},
author = {Andrei Moroianu and Gabriela Ovando},
journal= {arXiv preprint arXiv:2602.18373},
year = {2026}
}
Comments
21 pages