Natural Operations in Differential Geometry - Tapa blanda

Kolar, Ivan; Michor, Peter W.; Slovak, Jan

 
9783642081491: Natural Operations in Differential Geometry
Tapa blanda
ISBN 10: 3642081495 ISBN 13: 9783642081491
Editorial: Springer, 2010

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
3642081495
ISBN 13 
9783642081491
Encuadernación
Tapa blanda
Número de páginas
444
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9783540562351: Natural Operations in Differential Geometry

Edición Destacada

ISBN 10:  3540562354 ISBN 13:  9783540562351
Editorial: Springer, 1993
Tapa dura