Displaying similar documents to “Harmonic morphisms and circle actions on 3- and 4-manifolds”

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism f : M → N between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim M ≥ dim N , since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where d f vanishes. Every non-constant harmonic morphism is shown to be...

On generalized f -harmonic morphisms

A. Mohammed Cherif, Djaa Mustapha (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study the characterization of generalized f -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an f -harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144],...

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...

Biharmonic morphisms

Mustapha Chadli, Mohamed El Kadiri, Sabah Haddad (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let ( X , ℋ ) and ( X ' , ℋ ' ) be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from ( X , ℋ ) to ( X ' , ℋ ' ) is a continuous map from X to X ' which preserves the biharmonic structures of X and X ' . In the present work we study this notion and characterize in some cases the biharmonic morphisms between X and X ' in terms of harmonic morphisms between the harmonic spaces associated with ( X , ℋ ) and ( X ' , ℋ ' ) and the coupling kernels of them.