Skip to main content
SpringerLink
Log in

Differential Forms and Applications

  • Textbook
  • © 1994

Overview

Authors:
  1. Manfredo P. Carmo

    1. Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • well-established, easy-going introduction

Part of the book series: Universitext (UTX)

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 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
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-IX
    Download chapter PDF

  2. Differential Forms in Rn

    • Manfredo P. do Carmo
    Pages 1-16

  3. Line Integrals

    • Manfredo P. do Carmo
    Pages 17-31

  4. Differentiable Manifolds

    • Manfredo P. do Carmo
    Pages 33-54

  5. Integration on Manifolds; Stokes Theorem and Poincaré’s Lemma

    • Manfredo P. do Carmo
    Pages 55-75

  6. Differential Geometry of Surfaces

    • Manfredo P. do Carmo
    Pages 77-98

  7. The Theorem of Gauss-Bonnet and the Theorem of Morse

    • Manfredo P. do Carmo
    Pages 99-113

  8. Back Matter

    Pages 115-120
    Download chapter PDF
Back to top

Keywords

About this book

This is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome­ try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a complete hyperbolic plane in euclidean 3-space (Hilbert's theorem). For the present edition, we introduced a chapter on line integrals. In Chapter 1 we introduce the differential forms in Rn. We only assume an elementary knowledge of calculus, and the chapter can be used as a basis for a course on differential forms for "users" of Mathematics. In Chapter 2 we start integrating differential forms of degree one along curves in Rn. This already allows some applications of the ideas of Chapter 1. This material is not used in the rest of the book. In Chapter 3 we present the basic notions of differentiable manifolds. It is useful (but not essential) that the reader be familiar with the notion ofa regular surface in R3. In Chapter 4 we introduce the notion of manifold with boundary and prove Stokes theorem and Poincare's lemma. Starting from this basic material, we could follow any of the possi­ ble routes for applications: Topology, Differential Geometry, Mechanics, Lie Groups, etc. We have chosen Differential Geometry. For simplicity, we re­ stricted ourselves to surfaces.

Reviews

M.P. Do Carmo

Differential Forms and Applications

"This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. Each chapter is followed by interesting exercises. Thus, this is an ideal book for a one-semester course."—ACTA SCIENTIARUM MATHEMATICARUM

Authors and Affiliations

  • Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Manfredo P. Carmo

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation