Complex-valued harmonic morphisms on three-dimensional Euclidean space
This chapter presents an introduction to the theory of harmonic morphisms for the case of maps from open subsets of Euclidean 3-space to the complex plane. Harmonic morphisms are characterized by elementary means which involve only a little simple geometry. In subsequent chapters some of the results are generalized and interpreted the context of differential geometry. Some results apply to maps from open subsets of higher-dimensional Euclidean spaces to the complex plane, but many methods are special to Euclidean 3-space, in that case, giving us all harmonic morphisms both locally and globally.
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