| Natural Operations in Differential Geometry Contributor(s): Kolar, Ivan (Author), Michor, Peter W. (Author), Slovak, Jan (Author) |
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ISBN: 3642081495 ISBN-13: 9783642081491 Publisher: Springer OUR PRICE: $123.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Science | Physics - Quantum Theory - Computers | Information Technology |
| Dewey: 516.36 |
| Physical Information: 0.9" H x 6.14" W x 9.21" (1.36 lbs) 434 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |