Natural Operations in Differential Geometry

Ivan Kolar, Jan Slovak, Peter W. Michor

ISBN 10: 3540562354 / ISBN 13: 9783540562351

Editore: Springer Berlin Heidelberg, 1993

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Zustand: Gut | Sprache: Englisch | Produktart: Bücher.

Codice articolo 490417/203

Dati bibliografici

• Titolo: Natural Operations in Differential Geometry
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3540562354
• ISBN 13: 9783540562351
• Rilegatura: Rilegato
• Condizione: Gut
• Cataloghi dei venditori:
  • Bücher

Descrizione articolo

Riassunto

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.

Contenuti

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.