A note on harmonic maps between surfaces
Jürgen Jost (1985)
Annales de l'I.H.P. Analyse non linéaire
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Jürgen Jost (1985)
Annales de l'I.H.P. Analyse non linéaire
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Paul Baird (1987)
Annales de l'institut Fourier
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We study harmonic morphisms from domains in and to a Riemann surface , obtaining the classification of such in terms of holomorphic mappings from a covering space of into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of 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...
Simões, Bruno Ascenso (2010)
Journal of Inequalities and Applications [electronic only]
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Yun, Gabjin (2002)
International Journal of Mathematics and Mathematical Sciences
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S. Ianus, A.M. Pastore (1995)
Annales mathématiques Blaise Pascal
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Eric Loubeau, Radu Pantilie (2010)
Annales de l’institut Fourier
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We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being a harmonic morphism naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between...