Exterior Differential Systems and Equivalence Problems / Edition 1

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This monograph presents a concise yet elementary account of exterior differential system theory so that it can be quickly applied to problems. The first part of the monograph, Chapters 1-5, deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part of the monograph, Chapters 6 and 7, deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the O-R embedding problem is given, and embeddings of abstract projective structures are discussed.
For researchers and graduate students who would like a good introduction to exterior differential systems. This volume will also be particularly useful to those whose work involves differential geometry and partial differential equations.

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Product Details

  • ISBN-13: 9780792315933
  • Publisher: Springer Netherlands
  • Publication date: 3/31/1992
  • Series: Mathematics and Its Applications (closed) Series, #73
  • Edition description: 1992
  • Edition number: 1
  • Pages: 196
  • Product dimensions: 0.56 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Series Editor's Preface. 1. Exterior Algebra. II. Elementary Differential Systems. III. Cartan-Kaehler Theory. IV. Involution and Prolongation. V. Quasi-Linear Pfaffin Differential Systsems. VI. Higher Order G-Structures. VII. Embeddings of G-Structures. Bibliography. Index.

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