A note on the classification of holomorphic harmonic morphisms
The authors classify those holomorphic maps \(\varphi:U \to \mathbb{C}^ n\) defined on an open subset \(U \subset \mathbb{C}^ m\), which are harmonic morphisms. If \(n>1\) then \(\varphi\) is such a morphism iff it is an orthogonal projection followed by a homothety.
scientific article; zbMATH DE number 427952