Differentiable Manifolds : Forms, Currents, Harmonic Forms

Language: English

Published by Springer, Springer Gabler, 2011

3642617549 / 9783642617546

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduced by L. Schwartz, motivated the precise definition adopted here. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.

Seller Inventory # 9783642617546

Title
Differentiable Manifolds : Forms, Currents, Harmonic Forms
Author
Georges De Rham
Publisher
Springer, Springer Gabler
Publication year
2011
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642617549
ISBN 13
9783642617546
Item weight
289 grams
Dimensions
235x155x11 mm

AHA-BUCH GmbH

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