Self-duality and integrable systems
type: Item
instance of: scholarly article
title: Self-duality and integrable systems
zbMATH Open document ID: 0729.58030
author: Yousuke Ohyama
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: We consider the total space of self-dual connections and self-dual (i.e. the Weyl curvature is self-dual) metrics on a four-manifold. An infinite dimensional Lie algebra acts on this space transitively. Especially coordinate transformations of the corresponding twistor space act on the space of self-dual metrics, and gauge transformations act on the space of self-dual connections. In this sense composed systems of self-dual connections and self-dual metrics are completely integrable, and this integrability is equivalent to the integrability of complex structures of twistor spaces. This system can be considered as a deformation of D-modules in higher dimensions.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 35Q58
zbMATH DE Number: 4205447
zbMATH Keywords: KP equation
zbMATH Keywords: self-dual Yang-Mills equation
zbMATH Keywords: self-dual Einstein equation
zbMATH Keywords: integrable systems
zbMATH Keywords: self-dual manifold
zbMATH Keywords: self-dual connections
zbMATH Keywords: twistor space
zbMATH Keywords: self-dual metrics
reviewed by: Yoshiyuki Ohyama
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195170855
OpenAlex ID: W2077353282
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cites work: A new approach to the self-dual Yang-Mills equations
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DOI: 10.2977/PRIMS/1195170855
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description: scientific article; zbMATH DE number 4205447