Harmonic morphisms from the classical non-compact semisimple Lie groups

Details Harmonic morphisms from the classical non-compact semisimple Lie groups Harmonic morphisms from the classical non-compact semisimple Lie groups

2007-01-18

arxiv.org/abs/math/0701520v2

Mathematics

Differential Geometry

24 pages

Scientific paper

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.

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