Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups

2025/02/17 by Sigmundur Gudmundsson, Gudmundsson, Sigmundur, Thomas Jack Munn +1
Mathematics · #53C35 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2502.18492

openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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