Natural Operations in Differential Geometry

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

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.

Details

Published by: Springer

Publication Date: 1993-02-04

Format: Hardcover

ISBN-13: 9783540562351

DOI: 10.1007/978-3-662-02950-3

Dimensions: 234cm x156cm

Pages: 434