Natural Operations in Differential Geometry
Produktnummer:
184d679ed3480046cfa8a631b71926832c
| Autor: | Kolar, Ivan Michor, Peter W. Slovak, Jan |
|---|---|
| Themengebiete: | Category over Manifolds Jet Natural Bundle Natural Operator differential geometry manifold mathematical physics |
| Veröffentlichungsdatum: | 04.02.1993 |
| EAN: | 9783540562351 |
| Sprache: | Englisch |
| Seitenzahl: | 434 |
| Produktart: | Gebunden |
| Verlag: | Springer Berlin |
Produktinformationen "Natural Operations in Differential Geometry"
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.
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