Natural Operations in Differential Geometry PDF
by Ivan Kolar, Peter W. Michor, Jan Slovak
- Information
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.
Information
-
Download Now
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:09/03/2013
- Category:
- ISBN:9783662029503
Information
-
Download Now
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:09/03/2013
- Category:
- ISBN:9783662029503