Natural Operations in Differential Geometry (PDF)

Name: Natural Operations in Differential Geometry
Brand: Springer Berlin Heidelberg
SKU: 105056193
Price: 120.99 EUR
Availability: OnlineOnly

(Sprache: Englisch)

Autoren: Ivan Kolar , Peter W. Michor , Jan Slovak

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Natural Operations in Differential Geometry, 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.