Harmonic morphisms between riemannian manifolds
Annales de l'institut Fourier (1978)
- Volume: 28, Issue: 2, page 107-144
- ISSN: 0373-0956
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topFuglede, Bent. "Harmonic morphisms between riemannian manifolds." Annales de l'institut Fourier 28.2 (1978): 107-144. <http://eudml.org/doc/74351>.
@article{Fuglede1978,
abstract = {A harmonic morphism $f : M\rightarrow N$ between Riemannian manifolds $M$ and $N$ is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim$M\ge $ 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 $df$ vanishes. Every non-constant harmonic morphism is shown to be an open mapping.},
author = {Fuglede, Bent},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {107-144},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harmonic morphisms between riemannian manifolds},
url = {http://eudml.org/doc/74351},
volume = {28},
year = {1978},
}
TY - JOUR
AU - Fuglede, Bent
TI - Harmonic morphisms between riemannian manifolds
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 107
EP - 144
AB - A harmonic morphism $f : M\rightarrow N$ between Riemannian manifolds $M$ and $N$ is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim$M\ge $ 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 $df$ vanishes. Every non-constant harmonic morphism is shown to be an open mapping.
LA - eng
UR - http://eudml.org/doc/74351
ER -
References
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