Exterior Differential Systems
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,...
| Main Authors: | , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1991, 1991
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| Edition: | 1st ed. 1991 |
| Series: | Mathematical Sciences Research Institute Publications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- §1. The Notion of Prolongation
- §2. Ordinary Prolongation
- §3. The Prolongation Theorem
- §4. The Process of Prolongation
- VII. Examples
- §1. First Order Equations for Two Functions of Two Variables
- §2. Finiteness of the Web Rank
- §3. Orthogonal Coordinates
- §4. Isometric Embedding
- VIII. Applications of Commutative Algebra and Algebraic Geometry to the Study of Exterior Differential Systems
- §1. Involutive Tableaux
- §2. The Cartan-Poincaré Lemma, Spencer Cohomology
- §3. The Graded Module Associated to a Tableau; Koszul Homology
- §4. The Canonical Resolution of an Involutive Module
- §5. Localization; the Proofs of Theorem 3.2 and Proposition 3.8
- §6. Proof of Theorem 3.8 in Chapter V; Guillemin’s Normal Form
- §7. The Graded Module Associated to a Higher Order Tableau
- IX. PartialDifferential Equations
- §1. An Integrability Criterion
- §2. Quasi-Linear Equations
- §3. Existence Theorems
- X. Linear Differential Operators
- §1. Formal Theory and Complexes
- §2. Examples
- §3. Existence Theorems for Elliptic Equations
- I. Preliminaries
- §1. Review of Exterior Algebra
- §2. The Notion of an Exterior Differential System
- §3. Jet Bundles
- II. Basic Theorems
- §1. Probenius Theorem
- §2. Cauchy Characteristics
- §3. Theorems of Pfaff and Darboux
- §4. Pfaffian Systems
- §5. Pfaffian Systems of Codimension Two
- III. Cartan-Kähler Theory
- §1. Integral Elements
- §2. The Cartan-Kähler Theorem
- §3. Examples
- IV. Linear Differential Systems
- §1. Independence Condition and Involution
- §2. Linear Differential Systems
- §3. Tableaux
- §4. Tableaux Associated to an Integral Element
- §5. Linear Pfaffian Systems
- §6. Prolongation
- §7. Examples
- §8. Families of Isometric Surfaces in Euclidean Space
- V. The Characteristic Variety
- §1. Definition of the Characteristic Variety of a Differential System
- §2. The Characteristic Variety for Linearc Pfaffian Systems; Examples
- §3. Properties of the Characteristic Variety
- VI. Prolongation Theory