Natural operations in differential geometry

書誌事項

Natural operations in differential geometry

Ivan Kolář, Peter W. Michor, Jan Slovák

Springer-Verlag, c1993

  • : gw
  • : us
  • : softcover

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注記

Includes bibliographical references (p. [417]-427) and indexes

内容説明・目次

内容説明

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.

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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詳細情報
  • NII書誌ID(NCID)
    BA1976600X
  • ISBN
    • 3540562354
    • 0387562354
    • 9783642081491
  • LCCN
    92045829
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin ; New York
  • ページ数/冊数
    vi, 434 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
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