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  • Book
  • © 1983

Differential Geometry in the Large

Seminar Lectures New York University 1946 and Stanford University 1956

Authors:

  1. Heinz Hopf

    1. Eidgenössische Technische Hochschule Zürich, Switzerland

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1000)

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Table of contents (14 chapters)

  1. Front Matter

    Pages N2-VII
    PDF

  2. Selected Topics in Geometry

    1. Front Matter

      Pages 1-1
      PDF

  3. Differential Geometry in the Large

    1. Front Matter

      Pages 77-80
      PDF

    2. Introduction

      • Heinz Hopf
      Pages 81-81

    10. The Congruence Theorem for Ovaloids

      • Heinz Hopf
      Pages 163-173

  4. Back Matter

    Pages 185-187
    PDF
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About this book

These notes consist of two parts: 1) Selected Topics in Geometry, New York University 1946, Notes by Peter Lax. 2) Lectures on Differential Geometry in the Large, Stanford University 1956, Notes by J. W. Gray. They are reproduced here with no essential change. Heinz Hopf was a mathematician who recognized important mathema­ tical ideas and new mathematical phenomena through special cases. In the simplest background the central idea or the difficulty of a problem usually becomes crystal clear. Doing geometry in this fashion is a joy. Hopf's great insight allows this approach to lead to serious ma­ thematics, for most of the topics in these notes have become the star­ ting-points of important further developments. I will try to mention a few. It is clear from these notes that Hopf laid the emphasis on poly­ hedral differential geometry. Most of the results in smooth differen­ tial geometry have polyhedral counterparts, whose understanding is both important and challenging. Among recent works I wish to mention those of Robert Connelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri­ gidity, Proceedings of International Congress of Mathematicians, Hel­ sinki 1978, vol. 1, 407-414 ) • A theory of area and volume of rectilinear'polyhedra based on de­ compositions originated with Bolyai and Gauss.
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Keywords

  • Geometrie
  • Geometry
  • Globale Differentialgeometrie
  • curvature
  • differential geometry
  • Gaussian curvature
  • Mean curvature
  • Riemannian manifold
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Authors and Affiliations

  • Eidgenössische Technische Hochschule Zürich, Switzerland

    Heinz Hopf

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Bibliographic Information

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Access via your institution

Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

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