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The geometry of jet bundles /
The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1989.
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| Colección: | London Mathematical Society lecture note series ;
142. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Introduction; 1 Bundles; 1.1 Fibred Manifolds and Bundles; 1.2 Sections; 1.3 Bundle Morphisms; 1.4 New Bundles From Old; 2 Linear Bundles; 2.1 Vector Bundles; 2.2 Vector Bundle Morphisms; 2.3 Duality and Tensor Products; 2.4 Affine Bundles; 3 Linear Operations on General Bundles; 3.1 Tangent and Cotangent Vectors; 3.2 Vector Fields; 3.3 Differential Forms; 3.4 Derivations; 3.5 Connections; 4 First-order Jet Bundles; 4.1 First-order Jets; 4.2 Prolongations of Morphisms; 4.3 Total Derivatives and Contact Forms; 4.4 Prolongations of Vector Fields
- 4.5 The Contact Structure4.6 Jet Fields; 4.7 Vertical Lifts; 5 Second-order Jet Bundles; 5.1 Second-order Jets; 5.2 Repeated Jets; 5.3 Integrability and Semi-holonomic Jets; 5.4 Second-order Jet Fields; 5.5 The Cartan Form; 6 Higher-order Jet Bundles; 6.1 Multi-index Notation; 6.2 Higher-order Jets; 6.3 The Contact Structure; 6.4 Vector Fields and their Prolongations; 6.5 The Higher-order Cartan Form; 7 Infinite Jet Bundles; 7.1 Preliminaries; 7.2 Infinite Jets; 7.3 The Infinite Contact System; 7.4 The Inverse Problem; Bibliography; Glossary of Symbols; Index