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.
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Gudmundsson, S., Sakovich, A. Harmonic morphisms from the classical compact semisimple Lie groups. Ann Glob Anal Geom 33, 343–356 (2008). https://doi.org/10.1007/s10455-007-9090-8
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DOI: https://doi.org/10.1007/s10455-007-9090-8