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Differential Geometry: Manifolds, Curves, and Surfaces

Manifolds, Curves, and Surfaces

  • Textbook
  • © 1988

Overview

Authors:
  1. Marcel Berger

    1. I.H.E.S., Bures-sur-Yvette, France

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  2. Bernard Gostiaux

    1. Le Perreux, France

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 115)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
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  2. Background

    • Marcel Berger, Bernard Gostiaux
    Pages 1-29

  3. Differential Equations

    • Marcel Berger, Bernard Gostiaux
    Pages 30-46

  4. Differentiable Manifolds

    • Marcel Berger, Bernard Gostiaux
    Pages 47-102

  5. Partitions of Unity, Densities and Curves

    • Marcel Berger, Bernard Gostiaux
    Pages 103-127

  6. Critical Points

    • Marcel Berger, Bernard Gostiaux
    Pages 128-145

  7. Differential Forms

    • Marcel Berger, Bernard Gostiaux
    Pages 146-187

  8. Integration of Differential Forms

    • Marcel Berger, Bernard Gostiaux
    Pages 188-243

  9. Degree Theory

    • Marcel Berger, Bernard Gostiaux
    Pages 244-276

  10. Curves: The Local Theory

    • Marcel Berger, Bernard Gostiaux
    Pages 277-311

  11. Plane Curves: The Global Theory

    • Marcel Berger, Bernard Gostiaux
    Pages 312-345

  12. A Brief Guide to the Local Theory of Surfaces in R3

    • Marcel Berger, Bernard Gostiaux
    Pages 346-402

  13. A Brief Guide to the Global Theory of Surfaces

    • Marcel Berger, Bernard Gostiaux
    Pages 403-441

  14. Back Matter

    Pages 443-476
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Keywords

About this book

This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ­ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc­ tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

Authors and Affiliations

  • I.H.E.S., Bures-sur-Yvette, France

    Marcel Berger

  • Le Perreux, France

    Bernard Gostiaux

Bibliographic Information

  • Book Title: Differential Geometry: Manifolds, Curves, and Surfaces

  • Book Subtitle: Manifolds, Curves, and Surfaces

  • Authors: Marcel Berger, Bernard Gostiaux

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1033-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-387-96626-7Published: 23 November 1987

  • Softcover ISBN: 978-1-4612-6992-2Published: 02 October 2012

  • eBook ISBN: 978-1-4612-1033-7Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 476

  • Additional Information: Original French edition published by Presses Universitaires de France -PUF

  • Topics: Differential Geometry

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