Displaying similar documents to “Quaternionic maps and minimal surfaces”

Hörmander systems and harmonic morphisms

Elisabetta Barletta (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Given a Hörmander system X = { X 1 , ⋯ , X m } on a domain Ω ⊆ 𝐑 n we show that any subelliptic harmonic morphism φ from Ω into a ν -dimensional riemannian manifold N is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also φ is a submersion provided that ν ≤ m and X has rank m . If Ω = 𝐇 n (the Heisenberg group) and X = 1 2 L α + L α ¯ , 1 2 i L α - L α ¯ , where L α ¯ = ∂ / ∂ z ¯ α - i z α ∂ / ∂ t is the Lewy operator, then a smooth map φ : Ω → N is a subelliptic harmonic morphism if and only if φ ∘ π : ( C ( 𝐇 n ) , F θ 0 ) → N is a harmonic morphism, where S 1 → C ( 𝐇 n ) → π → 𝐇 n is the canonical circle bundle and F θ 0 ...

Harmonic morphisms onto Riemann surfaces and generalized analytic functions

Paul Baird (1987)

Annales de l'institut Fourier

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We study harmonic morphisms from domains in R 3 and S 3 to a Riemann surface N , obtaining the classification of such in terms of holomorphic mappings from a covering space of N into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of S 3 to a Riemann surface is essentially the Hopf map. Comparison is made with the theory of analytic functions. In particular we consider multiple-valued harmonic morphisms defined on domains...