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A Course in Differential Geometry

  • Textbook
  • © 1978

Overview

Authors:
  1. Wilhelm Klingenberg

    1. Mathematisches Institut der Universität Bonn, Bonn, West Germany

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 51)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Calculus in Euclidean Space

    • Wilhelm Klingenberg
    Pages 1-7

  3. Curves

    • Wilhelm Klingenberg
    Pages 8-20

  4. Plane Curves: Global Theory

    • Wilhelm Klingenberg
    Pages 21-32

  5. Surfaces: local theory

    • Wilhelm Klingenberg
    Pages 33-72

  6. Intrinsic Geometry of Surfaces: Local Theory

    • Wilhelm Klingenberg
    Pages 73-88

  7. Two-Dimensional Riemannian Geometry

    • Wilhelm Klingenberg
    Pages 89-122

  8. The Global Geometry of Surfaces

    • Wilhelm Klingenberg
    Pages 123-166

  9. Back Matter

    Pages 167-180
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Keywords

About this book

This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin­ ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.

Authors and Affiliations

  • Mathematisches Institut der Universität Bonn, Bonn, West Germany

    Wilhelm Klingenberg

Bibliographic Information

  • Book Title: A Course in Differential Geometry

  • Authors: Wilhelm Klingenberg

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-9923-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1978

  • Softcover ISBN: 978-1-4612-9925-7Published: 22 January 2013

  • eBook ISBN: 978-1-4612-9923-3Published: 14 March 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 180

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: The German original edition was published as Band 107 of the series: Heidelberger Taschenbücher

  • Topics: Differential Geometry

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