Get 40% off our selection of bestselling print books in Engineering through October 31st!

Grundlehren der mathematischen Wissenschaften

Differentiable Manifolds

Forms, Currents, Harmonic Forms

Authors: Rham, Georges de

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-61752-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-61754-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (6 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-61752-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-61754-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Differentiable Manifolds
Book Subtitle
Forms, Currents, Harmonic Forms
Authors
Translated by
Smith, F.R.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
266
Copyright
1984
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-61752-2
DOI
10.1007/978-3-642-61752-2
Softcover ISBN
978-3-642-61754-6
Series ISSN
0072-7830
Edition Number
1
Number of Pages
X, 170
Additional Information
Title of the original French edition: Varietes differentiables
Topics