Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups

Sigmundur Gudmundsson; Thomas Jack Munn

Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups

Differential Geometry 2025-07-25 v2

Authors: Sigmundur Gudmundsson , Thomas Jack Munn

Abstract

Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$ . We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic.

Keywords

foliations lie groups holonomy

Cite

@article{arxiv.2502.18492,
  title  = {Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups},
  author = {Sigmundur Gudmundsson and Thomas Jack Munn},
  journal= {arXiv preprint arXiv:2502.18492},
  year   = {2025}
}

Comments

arXiv admin note: text overlap with arXiv:2308.15971

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