Mathematical Sciences Research Institute Publications

Exterior Differential Systems

Authors: Bryant, R.L., Chern, S.S., Gardner, R.B., Goldschmidt, H.L., Griffiths, P.A.

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About this book

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.

Table of contents (1 chapter)

  • Cartan-Kähler Theory

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

    Pages 58-101

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Buy this book

eBook $89.99 net
( price for USA )
  • ISBN 978-1-4613-9714-4
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $119.00 net
( price for USA )
  • ISBN 978-1-4613-9716-8
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Exterior Differential Systems
Series Title
Mathematical Sciences Research Institute Publications
Series Volume
18
Copyright
1991
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9714-4
DOI
10.1007/978-1-4613-9714-4
Softcover ISBN
978-1-4613-9716-8
Series ISSN
0940-4740
Edition Number
1
Topics