Harmonic morphisms from the classical compact semisimple Lie groups

Abstract

In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups $${\bf SL}_n({\mathbb{R}})$$ , SU *(2n), $${\bf Sp}(n, {\mathbb{R}})$$ , SO *(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics.