Download This PDF Book: Natural Operations in Differential Geometry by Ivan Kolar, Peter W. Michor, Jan Slovak , for free.
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.
TABLE OF CONTENTS:
CHAPTER I.MANIFOLDS AND LIE GROUPS
CHAPTER II.DIFFERENTIAL FORMS
CHAPTER III.BUNDLES AND CONNECTIONS
CHAPTER IV.JETS AND NATURAL BUNDLES
CHAPTER V.FINITE ORDER THEOREMS
CHAPTER VI.METHODS FOR FINDING NATURAL OPERATORS
CHAPTER VII.FURTHER APPLICATIONS
CHAPTER VIII.PRODUCT PRESERVING FUNCTORS
CHAPTER IX.BUNDLE FUNCTORS ON MANIFOLDS
CHAPTER X.PROLONGATION OF VECTOR FIELDS AND CONNECTIONS
CHAPTER XI.GENERAL THEORY OF LIE DERIVATIVES
CHAPTER XII.GAUGE NATURAL BUNDLES AND OPERATORS
About The Book:
Publisher : Springer, (February 4, 1993)
Language : English
Pages : 440
File: PDF, 10 MB
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