Group actions, gauge transformations, and the calculus of variations
type: Item
instance of: scholarly article
title: Group actions, gauge transformations, and the calculus of variations
zbMATH Open document ID: 0772.53011
DOI: 10.1007/BF01444737
author: Jürgen Jost
author: Xiao-Wei Peng
published in: Mathematische Annalen
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/164978
review text: Let \(M\) be a Banach manifold with a smooth Riemannian metric and let \(G\) be a Banach Lie group acting isometrically on \(M\). Also, it is assumed that \(\varphi\) is a \(G\)-invariant smooth map from \(M\) into a Banach space. The present paper is devoted to the study of the geometry of \(M^ 0_ g = \varphi^{-1}(0)/G\). In particular, the authors study the Riemannian metric and curvature of \(M^ 0_ g\) induced by the metric of \(M\), using a variational problem for gauge transformations. Applications are dealing with the space of metrics or connections, especially the moduli space of self-dual connections on bundles over 4-manifolds, the Weil-Petersson metric on Teichmüller space and Hamiltonian group actions (\(\varphi\) being now a moment map).
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 58D17
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 126350
zbMATH Keywords: Banach manifold
zbMATH Keywords: Banach Lie group
zbMATH Keywords: Riemannian metric
zbMATH Keywords: curvature
zbMATH Keywords: Teichmüller space
reviewed by: E. Vassiliou
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 126350