Natural Operations in Differential Geometry

Ivan Kolar

ISBN 10: 3540562354 / ISBN 13: 9783540562351

Published by Springer, Springer Vieweg Feb 1993, 1993

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 444 pp. Englisch.

Seller Inventory # 9783540562351

Bibliographic Details

• Title: Natural Operations in Differential Geometry
• Publisher: Springer, Springer Vieweg Feb 1993
• Publication Date: 1993
• Language: English
• ISBN 10: 3540562354
• ISBN 13: 9783540562351
• Binding: Buch
• Condition: Neu
• Dimensions: 240W x 161H x 30D millimeters 240 millimeters width by 161 millimeters height by 30 millimeters depth
• Weight: 830 grams

About this title

Synopsis

The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op­ erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. 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.