Harmonic morphisms from the classical compact semisimple Lie groups

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

2006-11-19

arxiv.org/abs/math/0611574v3

Mathematics

Differential Geometry

14 pages; minor changes

Scientific paper

In this paper 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 SL(n,R), SU(2n), Sp(n,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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