English

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.

Keywords

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}
}

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21 pages