Harmonic morphisms and circle actions on 3- and 4-manifolds
type: Item
instance of: scholarly article
title: Harmonic morphisms and circle actions on 3- and 4-manifolds
zbMATH Open document ID: 0676.58023
author: Paul Baird
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74870
review text: 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 \(\phi\) : \(M\to N\) from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on M with possible fixed points. This restricts the topology of M. In all cases, a harmonic morphism \(\phi\) : \(M\to N\) from a closed \((n+1)\)-dimensional manifold to an n- dimensional manifold (n\(\geq 2\), with M,N analytic in the case \(n=2)\) determines a locally smooth circle action on M.
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 4107782
zbMATH Keywords: Harmonic morphisms
zbMATH Keywords: generalization of the analytic functions
zbMATH Keywords: analytic 3- manifold
MaRDI profile type: Publication
OpenAlex ID: W1996586446
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DOI: 10.5802/AIF.1210
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4107782