Exterior Differential Systems and Equivalence Problems / Edition 1

by Kichoon Yang

Overview

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.

Product Details

ISBN-13:	9780792315933
Publisher:	Springer Netherlands
Publication date:	03/31/1992
Series:	Mathematics and Its Applications , #73
Edition description:	1992
Pages:	196
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

I. Exterior Algebra.- II. Elementary Differential Systems.- III. Cartan-Kaehler Theory.- IV. Involution and Prolongation.- V. Quasi-Linear Pfaffian Differential Systems.- VI. Higher Order G-structures.- VII. Embeddings of G-structures.