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

Un morphisme harmonique f:M→N 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.

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 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.

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     author = {Fuglede, Bent},
     title = {Harmonic morphisms between riemannian manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {107--144},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     number = {2},
     year = {1978},
     doi = {10.5802/aif.691},
     mrnumber = {80h:58023},
     zbl = {0339.53026},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.691/}
}
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Fuglede, Bent. Harmonic morphisms between riemannian manifolds. Annales de l'Institut Fourier, Tome 28 (1978) no. 2, pp. 107-144. doi : 10.5802/aif.691. http://www.numdam.org/articles/10.5802/aif.691/

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