Natural Operations in Differential Geometry (Paperback)

Ivan Kolar

ISBN 10: 3642081495 / ISBN 13: 9783642081491

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2010

About this Item

Paperback. The literature on natural bundles and natural operators in differential geometry, was until now, scattered in the mathematical journal literature. This book is the first monograph on the subject, collecting this material in a unified presentation. The book begins with an introduction to differential geometry stressing naturality and functionality, and the general theory of connections on arbitrary fibered manifolds. The functional approach to classical natural bundles is extended to a large class of geometrically interesting categories. Several methods of finding all natural operators are given and these are identified for many concrete geometric problems. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces, and the basic structures from the theory of jets are therefore described here too in a self-contained manner. The relations of these geometric problems to corresponding questions in mathematical physics are brought out in several places in the book, and it closes with a very comprehensive bibliography of over 300 items.This book is a timely addition to literature filling the gap that existed here and will be a standard reference on natural operators for the next few years. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783642081491

Bibliographic Details

• Title: Natural Operations in Differential Geometry (Paperback)
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Publication Date: 2010
• Language: English
• ISBN 10: 3642081495
• ISBN 13: 9783642081491
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

Natural operators and natural operations are an area of differential geometry that relates closely to problems in theoretical physics. So far there has been no book on the subject. This one therefore fills the gap and collects in an unified presentation the otherwise scattered material on the subject; it also includes a very comprehensive bibliography and will certainly be the standard reference for the next few years.