Ivan Kolar, Peter W. Michor, Jan Slovak

Natural Operations in Differential Geometry

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-56235-1
• 1993.
• Seitenzahl: 444
• Erscheinungstermin: 4. Februar 1993
• Englisch
• Abmessung: 240mm x 161mm x 30mm
• Gewicht: 780g
• ISBN-13: 9783540562351
• ISBN-10: 3540562354
• Artikelnr.: 22925025

Inhaltsangabe

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.