The geometry of jet bundles / D.J. Saunders.

Format:

Book

Author/Creator:

Saunders, D. J., 1964- author.

Series:

London Mathematical Society lecture note series ; 142.

London Mathematical Society lecture note series ; 142

Language:

English

Subjects (All):

Jet bundles (Mathematics).

Geometry, Differential.

Physical Description:

1 online resource (293 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1989.

Language Note:

English

Summary:

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 jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. The book includes a proof of the local exactness of the variational bicomplex. A knowledge of differential geometry is assumed by the author, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. Coordinate-free techniques are used throughout, although coordinate representations are often used in proofs and when considering applications.

Contents:

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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 286-287) and index.

ISBN:

1-139-88630-4

1-107-36647-X

1-107-37118-X

1-107-36156-7

1-107-37019-1

1-299-40425-1

1-107-36401-9

0-511-52641-5