Connections with prescribed curvature
type: Item
instance of: scholarly article
title: Connections with prescribed curvature
zbMATH Open document ID: 0627.53027
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74779
review text: We discuss the problem of prescribing the curvature of a connection on a principal bundle whose base manifold is three-dimensional. In particular, we consider the local question: Given a curvature form F, when does there exist locally a connection A such that F is the curvature of A ? When the structure group of the bundle is semisimple, a finite number of nonlinear identities arise as necessary conditions for local solvability of the curvature equation. We conjecture that these conditions are also generically sufficient, and we prove this for bundles whose structure group is of low rank. Nilpotent structure groups are also discussed.
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 4019925
zbMATH Keywords: prescribed curvature
zbMATH Keywords: connection
zbMATH Keywords: principal bundle
zbMATH Keywords: nilpotent structure groups
author: Dennis DeTurck
author: Janet Talvacchia
MaRDI profile type: Publication
OpenAlex ID: W1986176393
cites work: Q3746527
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DOI: 10.5802/AIF.1109
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 4019925