Abstract
AbstractThe first section of this chapter investigates the general question of when holomorphic maps between almost Hermitian manifolds are harmonic maps or harmonic morphisms. In particular, a holomorphic map from a Kaehler manifold to a Riemann surface is always a harmonic morphism. It is shown how harmonic morphisms into a Riemann surface can sometimes be combined to give new ones. The construction of harmonic morphisms from domains of Euclidean and related spaces is discussed, which are holomorphic with respect to a Hermitian structure, thus finding interesting globally defined complex-valued harmonic morphisms on a Euclidean space of arbitrary dimension.
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