A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, 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 vanishes. Every non-constant harmonic morphism is shown to be an open mapping.
Un morphisme harmonique entre variétés riemanniennes et est par définition une application continue qui “remonte” les fonctions harmoniques. On suppose dim dim, 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 est nul. On montre que tout morphisme harmonique non constant est une application ouverte.
@article{AIF_1978__28_2_107_0,
author = {Fuglede, Bent},
title = {Harmonic morphisms between riemannian manifolds},
journal = {Annales de l'Institut Fourier},
pages = {107--144},
year = {1978},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {28},
number = {2},
doi = {10.5802/aif.691},
mrnumber = {80h:58023},
zbl = {0339.53026},
language = {en},
url = {https://www.numdam.org/articles/10.5802/aif.691/}
}
TY - JOUR AU - Fuglede, Bent TI - Harmonic morphisms between riemannian manifolds JO - Annales de l'Institut Fourier PY - 1978 SP - 107 EP - 144 VL - 28 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.691/ DO - 10.5802/aif.691 LA - en ID - AIF_1978__28_2_107_0 ER -
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
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