The Geometry of Jet Bundles

by D. J. Saunders

Overview

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.

Product Details

ISBN-13:	9780521369480
Publisher:	Cambridge University Press
Publication date:	03/09/1989
Series:	London Mathematical Society Lecture Note Series , #142
Pages:	304
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)

Table of Contents

Introduction; 1. Bundles; 2. Linear bundles; 3. Linear operations on general bundles; 4. First-order jet bundles; 5. Second-order jet bundles; 6. Higher-order jet bundles; 7. Infinite jet bundles; Bibliography; Glossary of symbols; Index.

Editorial Reviews

An introduction to the theory of jet bundles for mathematicians and physicists who wish to study, in a modern geometric way, differential equations, particularly those associated with the calculus of variations. A major theme proposes that jets may be considered as a natural generalization of vector fields for studying problems in field theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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