A gauge theoretic approach to Einstein 4-manifolds
type: Item
instance of: scholarly article
title: A gauge theoretic approach to Einstein 4-manifolds
zbMATH Open document ID: 1295.53038
author: Joel Fine
author: Kirill Krasnov
author: Dmitri Panov
published in: The New York Journal of Mathematics
publication date: 2014-04-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1312.2831
full work available at URL: 20-18.html
review text: The aim of the paper is the reformulation of Einstein's equations in dimension \(4\) in the language of gauge theory. The paper wants to describe constructions from physics in a language accessible to mathematicians. For a definite connection over a \(4\)-manifold, a metric is defined using the curvature of the connection. The connection can be viewed as the potential for the metric. To the connection, an action is associated (the volume of the metric) whose critical points are Einstein metrics. Topological bounds are also investigated and are related with the anti-self-dual property of the Einstein metric. The given reformulation of Einstein's equations gives a link between Einstein \(4\)-manifolds and other types of special manifolds. The formalism also gives a new variational approach to Einstein metrics, because the traditional action principle is not suitable for the calculus of variations.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C07
zbMATH DE Number: 6282912
zbMATH Keywords: Einstein manifold
zbMATH Keywords: gauge theory
reviewed by: Zdeněk Dušek
MaRDI profile type: Publication
arXiv ID: 1312.2831
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description: scientific article