Non-holomorphic harmonic morphisms from Kähler manifolds
type: Item
instance of: scholarly article
title: Non-holomorphic harmonic morphisms from Kähler manifolds
zbMATH Open document ID: 0826.53029
DOI: 10.1007/BF02568184
author: Sigmundur Gudmundsson
published in: Manuscripta Mathematica
publication date: 1995-11-14T00:00:00Z
full work available at URL: https://eudml.org/doc/156008
review text: Given a harmonic morphism \(\psi : N^2 \times M \to \Sigma^2\) in each variable separately, where \(N^2\), \(\Sigma^2\) are surfaces and \(M\) is Riemannian, it has been observed by \textit{J. C. Wood} and the author [Math. Scand. 73, No. 1, 127-155 (1993; Zbl 0790.58009)] that the local smooth solutions \(w = \varphi(p)\) of the equation \(\psi(w,p) = z_0\) define harmonic morphisms. In the present paper the author uses this in various contexts to produce nonholomorphic harmonic morphisms from Kähler manifolds, in particular, from complex Grassmannians.
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58C10
zbMATH DE Number: 722246
zbMATH Keywords: holomorphic maps
zbMATH Keywords: harmonic morphism
zbMATH Keywords: Grassmannians
reviewed by: Gábor Tóth
MaRDI profile type: Publication
cites work: Bernstein theorems for harmonic morphisms from \({\mathbb R}\) 3 and S 3
cites work: Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras
cites work: Twistor theory for Riemannian symmetric spaces. With applications to harmonic maps of Riemann surfaces
cites work: The construction of harmonic maps into complex Grassmannians
cites work: Q4023642
cites work: Transformation groups
cites work: Harmonic maps from surfaces to complex projective spaces
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: Q4836743
cites work: Harmonic morphisms between Riemannian manifolds
cites work: Multivalued harmonic morphisms.
cites work: A mapping of Riemannian manifolds which preserves harmonic functions
cites work: Über holomorphe Abbildungen projektiv-algebraischer Mannigfaltigkeiten auf komplexe Räume
cites work: Harmonic maps into Lie groups (classical solutions of the chiral model)
cites work: Harmonic sequences and harmonic maps of surfaces into complex Grassmannian manifolds
cites work: The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian.
description: scientific article; zbMATH DE number 722246