Author | Bryant, Robert L. author |
---|---|
Title | Exterior Differential Systems [electronic resource] / by Robert L. Bryant, S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P. A. Griffiths |
Imprint | New York, NY : Springer New York, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9714-4 |
Descript | VII, 475 p. online resource |
I. Preliminaries -- ยง1. Review of Exterior Algebra -- ยง2. The Notion of an Exterior Differential System -- ยง3. Jet Bundles -- II. Basic Theorems -- ยง1. Probenius Theorem -- ยง2. Cauchy Characteristics -- ยง3. Theorems of Pfaff and Darboux -- ยง4. Pfaffian Systems -- ยง5. Pfaffian Systems of Codimension Two -- III. Cartan-Kรคhler Theory -- ยง1. Integral Elements -- ยง2. The Cartan-Kรคhler Theorem -- ยง3. Examples -- IV. Linear Differential Systems -- ยง1. Independence Condition and Involution -- ยง2. Linear Differential Systems -- ยง3. Tableaux -- ยง4. Tableaux Associated to an Integral Element -- ยง5. Linear Pfaffian Systems -- ยง6. Prolongation -- ยง7. Examples -- ยง8. Families of Isometric Surfaces in Euclidean Space -- V. The Characteristic Variety -- ยง1. Definition of the Characteristic Variety of a Differential System -- ยง2. The Characteristic Variety for Linearc Pfaffian Systems; Examples -- ยง3. Properties of the Characteristic Variety -- VI. Prolongation Theory -- ยง1. The Notion of Prolongation -- ยง2. Ordinary Prolongation -- ยง3. The Prolongation Theorem -- ยง4. The Process of Prolongation -- VII. Examples -- ยง1. First Order Equations for Two Functions of Two Variables -- ยง2. Finiteness of the Web Rank -- ยง3. Orthogonal Coordinates -- ยง4. Isometric Embedding -- VIII. Applications of Commutative Algebra and Algebraic Geometry to the Study of Exterior Differential Systems -- ยง1. Involutive Tableaux -- ยง2. The Cartan-Poincarรฉ Lemma, Spencer Cohomology -- ยง3. The Graded Module Associated to a Tableau; Koszul Homology -- ยง4. The Canonical Resolution of an Involutive Module -- ยง5. Localization; the Proofs of Theorem 3.2 and Proposition 3.8 -- ยง6. Proof of Theorem 3.8 in Chapter V; Guilleminโs Normal Form -- ยง7. The Graded Module Associated to a Higher Order Tableau -- IX. Partial Differential Equations -- ยง1. An Integrability Criterion -- ยง2. Quasi-Linear Equations -- ยง3. Existence Theorems -- X. Linear Differential Operators -- ยง1. Formal Theory and Complexes -- ยง2. Examples -- ยง3. Existence Theorems for Elliptic Equations