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arXiv · 2502.18492

Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups

Sigmundur Gudmundsson·Thomas Jack Munn
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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.

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Sigmundur Gudmundsson, Thomas Jack Munn. 2025-02-17. Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups. https://arxiv.org/abs/2502.18492

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