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Natural Operations in Differential Geometry / by Ivan Kolar, Peter W. Michor, Jan Slovak
版 | 1st ed. 1993. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1993 |
本文言語 | 英語 |
大きさ | VI, 434 p : online resource |
著者標目 | *Kolar, Ivan author Michor, Peter W author Slovak, Jan author SpringerLink (Online service) |
件 名 | LCSH:Geometry, Differential LCSH:Spintronics LCSH:Geometry LCSH:Quantum physics FREE:Differential Geometry FREE:Spintronics FREE:Geometry FREE:Quantum Physics |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-02950-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783662029503 |
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EB00237986 |
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