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Natural Operations in Differential Geometry

Natural Operations in Differential Geometry (Paperback)

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Synopsis

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.

Science & MathematicsMathematicsGeometryAnalytic geometryScience & MathematicsMathematicsGeometryDifferential & Riemannian geometryScience & MathematicsPhysicsQuantum physics incl quantum mechanics & quantum field theory Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 01/12/2010 ISBN-13: 9783642081491  Details: Type: Paperback Format: Books
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