The theory of overdetermined linear systems and its applications to nonlinear field equations
type: Item
instance of: scholarly article
title: The theory of overdetermined linear systems and its applications to nonlinear field equations
zbMATH Open document ID: 0596.35097
DOI: 10.1016/0393-0440(84)90008-1
author: Michel Dubois-Violette
published in: Journal of Geometry and Physics
publication date: 1984-01-01T00:00:00Z
review text: The paper contains a review of Spencer cohomology for linear systems of partial differential equations with many illustrating examples. The integrability condition for such a linear system is a system of nonlinear partial differential equations for the coefficients of the linear system which expresses the vanishing of Spencer cohomology classes of this linear system. This is used to produce linear systems such that their integrability conditions are just the Einstein's equation, the Yang-Mills equations or some other nonlinear equations of geometrical or of physical relevance. It is shown, in particular, that the Einstein and the Yang- Mills equations are equivalent to the vanishing of the curvature of some connections on appropriate vector bundles.
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 58J99
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 35F05
zbMATH DE Number: 3960119
zbMATH Keywords: Spencer cohomology
zbMATH Keywords: integrability condition
zbMATH Keywords: Einstein's equation
zbMATH Keywords: Yang- Mills equations
MaRDI profile type: Publication
full work available at URL: 0393-0440(84)90008-1
OpenAlex ID: W2025750416
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Wikidata QID: Q126179107
description: scientific article; zbMATH DE number 3960119