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Geometry of Manifolds with Non-negative Sectional Curvature pp 117–196Cite as

An Introduction to Exterior Differential Systems

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2110))

Abstract

An exterior differential system is by definition a partial differential equation for submanifolds formulated in the language of differential forms. In this introduction we construct the contact systems on several kinds of jet bundles in order to reduce general partial differential equations to exterior differential systems. Moreover we discuss the algebraic properties of the Spencer cohomology associated to an exterior differential system and sketch a proof of the theorem of Cartan–Kähler about the analytical solutions to an analytical exterior differential system.

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References

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Authors and Affiliations

  1. Instituto de Matemáticas (Cuernavaca), Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Lomas de Chamilpa, 62210, Cuernavaca, Morelos, Mexico

    Gregor Weingart

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  1. Gregor Weingart
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Correspondence to Gregor Weingart .

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Weingart, G. (2014). An Introduction to Exterior Differential Systems. In: Geometry of Manifolds with Non-negative Sectional Curvature. Lecture Notes in Mathematics, vol 2110. Springer, Cham. https://doi.org/10.1007/978-3-319-06373-7_6

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