Harmonic maps and harmonic morphisms

A harmonic morphism is a map between Riemannian manifolds which preserves Laplace's equation. We compare the properties of harmonic morphisms with those of the better known harmonic maps, seeing that they behave in some ways “dual” to the latter. In particular, we give representation theorems for harmonic morphisms in low dimensions which suggest that the equations might be soluble in some cases by integrable-system techniques in a similar way to that used in harmonic map theory. Bibl. 38 titles.