Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on with possible fixed points. This restricts the topology of . In all cases, a harmonic morphism from a closed -dimensional manifold to an -dimensional manifold (n, with , analytic in the case determines a locally smooth circle action on .
On considère les morphismes harmoniques comme généralisation naturelle des fonctions analaytiques qu’on rencontre dans la théorie des surfaces de Riemann. On montre que chaque variété fermée et analytique à 3 dimensions qui supporte un morphisme harmonique à valeurs dans une surface de Riemann est un espace fibré de Seifert. On étudie les morphismes harmoniques définies sur une variété fermée à 4 dimensions et à valeurs dans une variété à 3 dimensions. Ceux-ci déterminent une action du cercle sur qui est localement différentiable, peut-être avec des points fixes. Par conséquent la topologie de est limitée. Dans chaque cas, un morphisme harmonique défini sur une variété fermée à dimensions et à valeurs dans une variété à dimensions (, avec , analytiques dans le cas où ) détermine une action du cercle sur qui est localement différentiable.
@article{AIF_1990__40_1_177_0, author = {Baird, Paul}, title = {Harmonic morphisms and circle actions on 3- and 4-manifolds}, journal = {Annales de l'Institut Fourier}, pages = {177--212}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {40}, number = {1}, year = {1990}, doi = {10.5802/aif.1210}, zbl = {0676.58023}, mrnumber = {91e:57025}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1210/} }
TY - JOUR AU - Baird, Paul TI - Harmonic morphisms and circle actions on 3- and 4-manifolds JO - Annales de l'Institut Fourier PY - 1990 SP - 177 EP - 212 VL - 40 IS - 1 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1210/ DO - 10.5802/aif.1210 LA - en ID - AIF_1990__40_1_177_0 ER -
%0 Journal Article %A Baird, Paul %T Harmonic morphisms and circle actions on 3- and 4-manifolds %J Annales de l'Institut Fourier %D 1990 %P 177-212 %V 40 %N 1 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1210/ %R 10.5802/aif.1210 %G en %F AIF_1990__40_1_177_0
Baird, Paul. Harmonic morphisms and circle actions on 3- and 4-manifolds. Annales de l'Institut Fourier, Volume 40 (1990) no. 1, pp. 177-212. doi : 10.5802/aif.1210. https://aif.centre-mersenne.org/articles/10.5802/aif.1210/
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