Skip to main content
SpringerLink
Log in
Book cover

Differentiable Manifolds

Forms, Currents, Harmonic Forms

  • Book
  • © 1984

Overview

Authors:
  1. Georges Rham

    1. Lausanne, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 266)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Introduction

    • Georges de Rham
    Pages 1-2

  3. Notions About Manifolds

    • Georges de Rham
    Pages 3-14

  4. Differential Forms

    • Georges de Rham
    Pages 15-33

  5. Currents

    • Georges de Rham
    Pages 34-78

  6. Homologies

    • Georges de Rham
    Pages 79-98

  7. Harmonic Forms

    • Georges de Rham
    Pages 99-160

  8. Back Matter

    Pages 161-167
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • Lausanne, Switzerland

    Georges Rham

Bibliographic Information

  • Book Title: Differentiable Manifolds

  • Book Subtitle: Forms, Currents, Harmonic Forms

  • Authors: Georges Rham

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-61752-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1984

  • Softcover ISBN: 978-3-642-61754-6Published: 12 October 2011

  • eBook ISBN: 978-3-642-61752-2Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: X, 170

  • Additional Information: Title of the original French edition: Varietes differentiables

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

Publish with us

Policies and ethics

Back to top

Search

Navigation