Twistor spaces of Hyperkähler manifolds with \(S^{1}\)-actions.
type: Item
instance of: scholarly article
title: Twistor spaces of Hyperkähler manifolds with \(S^{1}\)-actions.
zbMATH Open document ID: 1069.53045
DOI: 10.1016/S0926-2245(03)00013-5
author: Birte Feix
published in: Differential Geometry and its Applications
publication date: 2003-08-25T00:00:00Z
review text: A hyper-Kähler structure consists of a triple of anti-commuting complex structures compatible with a fixed metric which is Kähler for all of them. Such manifolds admit a natural twistor space construction. In the present paper the author considers the structure of hyper-Kähler manifolds \(M\) admitting an \(S^1\)-action with the following properties: It is holomorphic with respect to one of the stuctures, scales the Kähler forms of the other two and its fixed point set is of dimension \({1\over 2}(\dim M)\). Then, there is a neighborhood of the fixed point set \(X\), such that the hyper-Kähler structure looks locally as a one on the cotangent bundle \(T^*X\) which is compatible with its holomorphic symplectic structure. Moreover, such structure is unique locally. The results are proven using analysis of the fixed point set and the structure of the corresponding twistor space.
Mathematics Subject Classification ID: 53C26
zbMATH DE Number: 1970810
zbMATH Keywords: Hyper-Kähler manifolds
zbMATH Keywords: Twistor space
zbMATH Keywords: Cotangent bundle
Wikidata QID: Q115338059
reviewed by: Gueo Grantcharov
MaRDI profile type: Publication
cites work: Q4040102
cites work: Hyperkähler metrics on cotangent bundles
cites work: Hyper-Kähler quotient construction of BPS monopole moduli spaces
cites work: The Self-Duality Equations on a Riemann Surface
cites work: Hyperkähler metrics and supersymmetry
cites work: Q4003058
description: scientific article; zbMATH DE number 1970810