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Geometry III

Theory of Surfaces

  • Book
  • © 1992

Overview

Editors:
  1. Yu. D. Burago

    1. LOMI, St. Petersburg, Russia

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  2. V. A. Zalgaller

    1. LOMI, St. Petersburg, Russia

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 48)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-vii
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  2. The Geometry of Surfaces in Euclidean Spaces

    • Yu. D. Burago, S. Z. Shefel’
    Pages 1-85

  3. Surfaces of Negative Curvature

    • E. R. Rozendorn
    Pages 87-178

  4. Local Theory of Bendings of Surfaces

    • I. Kh. Sabitov
    Pages 179-250

  5. Back Matter

    Pages 251-258
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Keywords

About this book

The original version of this article was written more than fiveyears ago with S. Z. Shefel',a profound and original mathematician who died in 1984. Sincethen the geometry of surfaces has continued to be enriched with ideas and results. This has required changes and additions, but has not influenced the character of the article, the design ofwhich originated with Shefel'. Without knowing to what extent Shefel' would have approved the changes, I should nevertheless like to dedicate this article to his memory. (Yu. D. Burago) We are trying to state the qualitative questions of the theory of surfaces in Euclidean spaces in the form in which they appear to the authors at present. This description does not entirely correspond to the historical development of the subject. The theory of surfaces was developed in the first place mainly as the 3 theory of surfaces in three-dimensional Euclidean space E ; however, it makes sense to begin by considering surfaces F in Euclidean spaces of any dimension n~ 3. This approach enables us, in particular, to put in a new light some 3 unsolved problems of this developed (and in the case of surfaces in E fairly complete) theory, and in many cases to refer to the connections with the present stage ofdevelopment of the theory of multidimensional submanifolds. The leading question of the article is the problem of the connection between classes of metrics and classes of surfaces in En.

Editors and Affiliations

  • LOMI, St. Petersburg, Russia

    Yu. D. Burago, V. A. Zalgaller

Bibliographic Information

  • Book Title: Geometry III

  • Book Subtitle: Theory of Surfaces

  • Editors: Yu. D. Burago, V. A. Zalgaller

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-02751-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Hardcover ISBN: 978-3-540-53377-1Published: 08 October 1992

  • Softcover ISBN: 978-3-642-08102-6Published: 01 December 2010

  • eBook ISBN: 978-3-662-02751-6Published: 14 March 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VIII, 258

  • Additional Information: Original Russian edition published by Publisher VINITI, Moscow, 1989

  • Topics: Differential Geometry

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