Hypercomplex structures associated to quaternionic manifolds
type: Item
instance of: scholarly article
title: Hypercomplex structures associated to quaternionic manifolds
zbMATH Open document ID: 0920.53018
DOI: 10.1016/S0926-2245(98)00026-6
published in: Differential Geometry and its Applications
publication date: 1999-09-19T00:00:00Z
review text: If \(M\) is a quaternionic manifold and \(P\) is an \(S^1\)-instanton over \(M\), then \textit{D. D. Joyce} [J. Differ. Geom. 35, 743-761 (1992; Zbl 0735.53050)] constructed a hypercomplex manifold we call \({\mathcal P}(M)\) over \(M\). These hypercomplex manifolds admit a \(U(2)\)-action of a special type permuting the complex structures. We show that up to double covers, all such hypercomplex manifolds arise in this way. Examples, including that of a hypercomplex structure on \(SU(3)\), show the necessity of including double covers of \({\mathcal P}(M)\).
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53C56
zbMATH DE Number: 1308136
zbMATH Keywords: instanton
zbMATH Keywords: self-duality
zbMATH Keywords: \(U(2)\)-symmetry
zbMATH Keywords: quaternionic manifold
zbMATH Keywords: hypercomplex manifold
author: Henrik Pedersen
author: Yat-Sun Poon
author: Andrew Swann
Wikidata QID: Q115337466
MaRDI profile type: Publication
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full work available at URL: s0926-2245(98)00026-6
OpenAlex ID: W2026218351
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description: scientific article; zbMATH DE number 1308136