Now in its second edition, this book provides a detailed introduction to the theory of jet bundles. It is written for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. A knowledge of differential geometry is assumed, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. The book explores how 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. It features a proof of the local exactness of the variational bicomplex. This edition includes new chapters on velocity bundles and bundles of contact elements, together with updated material on the calculus of variations.
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An updated introduction to the theory of jet bundles, including new chapters on velocity bundles and bundles of contact elements.
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;
8. Velocity bundles;
9.
Jet groups and bundles of contact elements; Bibliography; Glossary of
notation; Index.
D. J. Saunders, now retired, was most recently a visiting professor at the University of Ostrava in Czechia. He was joint editor (with Demeter Krupka) of 'Handbook of Global Analysis' (2008), which won the Rector's Prize at Palacký University, Olomouc, Czechia.
