Twistor geometry for hyperkähler metrics on complex adjoint orbits
type: Item
instance of: scholarly article
title: Twistor geometry for hyperkähler metrics on complex adjoint orbits
zbMATH Open document ID: 0924.53034
DOI: 10.1023/A:1006567614081
author: Sérgio D'Amorim Santa-Cruz
published in: Annals of Global Analysis and Geometry
publication date: 1999-11-08T00:00:00Z
review text: The author proposes a twistor approach for constructing hyperkähler metrics on complex semisimple adjoint orbits motivated by works of \textit{D. Burns} [Aspects Math. E9, 51-67 (1986; Zbl 0596.53057)] and \textit{P. B. Kronheimer} [J. Lond. Math. Soc., II. Ser. 42, 193-208 (1990; Zbl 0721.22006)]. He defines the twistor space as the union of certain regular adjoint orbits and exhibits a family of twistor lines. He also gives an algebraic characterization of the twistor lines. Finally, he discusses a construction of hyperkähler metrics by means of the identification, at least locally, of an adjoint orbit with the parameter space of twistor lines of its twistor space.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 32L25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1080035
zbMATH Keywords: adjoint orbits
zbMATH Keywords: hyper-Kähler metrics
zbMATH Keywords: twistor spaces
reviewed by: Johann Davidov
MaRDI profile type: Publication
full work available at URL: a:1006567614081
OpenAlex ID: W68671443
description: scientific article; zbMATH DE number 1080035