Harmonic morphisms from the classical non-compact semisimple Lie groups

2007/01/18 by Sigmundur Gudmundsson, Gudmundsson, Sigmundur, Anna Sakovich +1
Mathematics · #53C12 #53C43 #58E20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #math.DG #msc:53C12 #msc:53C43 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0701520

24 pages

openalex publication_date 2007/01/18 · arxiv created 2007/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct the first known complex valued harmonic morphisms from the non-compact Lie groups SL(n,R), SU*(2n) and Sp(n,R) equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.

Related

• Harmonic morphisms from the classical compact semisimple Lie groups
• Proper p-harmonic functions and harmonic morphisms on the classical\n non-compact semi-Riemannian Lie groups
• Harmonic morphisms from solvable Lie groups
• Proper r-harmonic functions from Riemannian manifolds
• Harmonic morphisms from homogeneous Hadamard manifolds