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Differential Geometry in the Large

Seminar Lectures New York University 1946 and Stanford University 1956

  • Heinz Hopf

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

Table of contents

About this book

Introduction

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.

Keywords

Geometrie Geometry Globale Differentialgeometrie curvature differential geometry Gaussian curvature Mean curvature Riemannian manifold

Authors and affiliations

  • Heinz Hopf
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-21563-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1983
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-12004-9
  • Online ISBN 978-3-662-21563-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
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