Harmonic morphisms between riemannian manifolds
Annales de l'Institut Fourier, Volume 28 (1978) no. 2, pp. 107-144.

A harmonic morphism f:MN between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dimM dimN, 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 df vanishes. Every non-constant harmonic morphism is shown to be an open mapping.

Un morphisme harmonique f:MN entre variétés riemanniennes M et N est par définition une application continue qui “remonte” les fonctions harmoniques. On suppose dimM dimN, puisque autrement tout morphisme harmonique est constant. On montre qu’un morphisme harmonique n’est autre qu’une application harmonique au sens de Eells et Sampson qui, en outre est semi-conforme, c’est-à-dire est une submersion conforme hors des points ou df est nul. On montre que tout morphisme harmonique non constant est une application ouverte.

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     title = {Harmonic morphisms between riemannian manifolds},
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Fuglede, Bent. Harmonic morphisms between riemannian manifolds. Annales de l'Institut Fourier, Volume 28 (1978) no. 2, pp. 107-144. doi : 10.5802/aif.691. https://aif.centre-mersenne.org/articles/10.5802/aif.691/

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