HyperKähler and quaternionic Kähler geometry
type: Item
instance of: scholarly article
title: HyperKähler and quaternionic Kähler geometry
zbMATH Open document ID: 0711.53051
DOI: 10.1007/BF01446581
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164790
review text: A (pseudo-) hyperKähler \((4n+4)\)-manifold \({\mathcal U}(M)\) is constructed for each quaternionic Kähler 4n-manifold in a way that is compatible with generalizations of the Marsden-Weinstein symplectic quotient. The manifold \({\mathcal U}(M)\) admits: (1) a certain type of SU(2)-action permuting the complex structures; (2) a function which is a Kähler potential for each complex structure; (3) quaternionic Kähler metrics in the same quaternionic class. Locally (1), (2) and (3) are equivalent and characterize \({\mathcal U}(M)\). Examples include, for a compact semisimple Lie group G, the nilpotent orbits in \({\mathfrak g}^{{\mathbb{C}}}\), which are seen to be fibred over quaternionic Kähler manifolds.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 4169614
zbMATH Keywords: quaternionic Kähler manifold
zbMATH Keywords: hyperKähler manifold
zbMATH Keywords: Marsden-Weinstein symplectic quotient
zbMATH Keywords: Kähler potential
zbMATH Keywords: semisimple Lie group
author: Andrew Swann
MaRDI profile type: Publication
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OpenAlex ID: W1966121613
description: scientific article; zbMATH DE number 4169614