| Autor: |
Ivan Kolar, Peter W. Michor, Jan Slovak |
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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. |
| Databáze: |
eBook Index |
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