The theory of overdetermined linear systems and its applications to nonlinear field equations
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.
scientific article; zbMATH DE number 3960119
scientific article