Displaying similar documents to “A geometric theory of harmonic and semi-conformal maps”

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 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...

Harmonic morphisms and circle actions on 3- and 4-manifolds

Paul Baird (1990)

Annales de l'institut Fourier

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Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms ϕ : M → N from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on M with possible fixed points. This restricts the topology of M . In all cases, a harmonic morphism ϕ : M → N from...