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Exterior Differential Systems

  • Robert L. Bryant
  • S. S. Chern
  • Robert B. Gardner
  • Hubert L. Goldschmidt
  • P. A. Griffiths

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 18)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 1-5
  3. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 6-26
  4. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 27-57
  5. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 58-101
  6. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 102-169
  7. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 170-235
  8. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 236-265
  9. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 266-312
  10. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 313-389
  11. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 390-416
  12. Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths
    Pages 417-461
  13. Back Matter
    Pages 462-475

About this book

Introduction

This book gives a treatment of exterior differential systems. It will in­ clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde­ pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen­ dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.

Keywords

Canon Lemma Web boundary element method character commutative property differential equation differential operator eXist equation form function manifold proposition theorem

Authors and affiliations

  • Robert L. Bryant
    • 1
  • S. S. Chern
    • 2
  • Robert B. Gardner
    • 3
  • Hubert L. Goldschmidt
    • 4
  • P. A. Griffiths
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Mathematical Sciences Research InstituteBerkeleyUSA
  3. 3.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  4. 4.Department of MathematicsColumbia UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9714-4
  • Copyright Information Springer-Verlag New York 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9716-8
  • Online ISBN 978-1-4613-9714-4
  • Series Print ISSN 0940-4740
  • Buy this book on publisher's site