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Natural Operations in Differential Geometry

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概要 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.続きを見る
目次 I. Manifolds and Lie Groups
II. Differential Forms
III. Bundles and Connections
IV. Jets and Natural Bundles
V. Finite Order Theorems
VI. Methods for Finding Natural Operators
VII. Further Applications
VIII. Product Preserving Functors
IX. Bundle Functors on Manifolds
X. Prolongation of Vector Fields and Connections
XI. General Theory of Lie Derivatives
XII. Gauge Natural Bundles and Operators
References
List of symbols
Author index.
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登録日 2014.09.18
更新日 2017.11.26