Publisher's Synopsis
This monograph presents a concise account of exterior differential system theory so that it can be quickly applied to problems. The first part 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 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 C-R embedding problem is given, and embeddings of abstract projective structures are discussed.;Aimed at researchers and graduate students who would like an introduction to exterior differential systems, this volume should also be useful to those whose work involves differential geometry and partial differential equations.
