Natural Operations in Differential Geometry is popular PDF and ePub book, written by Ivan Kolar in 2013-03-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Natural Operations in Differential Geometry can be Read Online from any device for your convenience.
Natural Operations in Differential Geometry Book PDF Summary
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.
Detail Book of Natural Operations in Differential Geometry PDF
- Author : Ivan Kolar
- Release : 09 March 2013
- Publisher : Springer Science & Business Media
- ISBN : 9783662029503
- Genre : Mathematics
- Total Page : 440 pages
- Language : English
- PDF File Size : 16,9 Mb
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