In mathematics, a harmonic morphism is a (smooth) map ϕ : ( M m , g ) → ( N n , h ) {\displaystyle \phi :(M^{m},g)\to (N^{n},h)} between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps, namely those that are horizontally (weakly) conformal.
In mathematics, a harmonic morphism is a (smooth) map ϕ : ( M m , g ) → ( N n , h ) {\displaystyle \phi :(M^{m},g)\to (N^{n},h)} between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps, namely those that are horizontally (weakly) conformal.
Source: Wikipedia "Harmonic morphism" · CC BY-SA 4.0
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