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Recent Synthetic Differential Geometry

  • Book
  • © 1970

Overview

Authors:
  1. Herbert Busemann

    1. University of Southern California, Los Angeles, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 54)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VII
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  2. Completeness, Finite Dimensionality, Differentiability

    • Herbert Busemann
    Pages 1-26

  3. Desarguesian Spaces

    • Herbert Busemann
    Pages 27-40

  4. Length Preserving Maps

    • Herbert Busemann
    Pages 41-55

  5. Geodesic

    • Herbert Busemann
    Pages 56-90

  6. Motions

    • Herbert Busemann
    Pages 91-100

  7. Observations on Method and Content

    • Herbert Busemann
    Pages 101-105

  8. Back Matter

    Pages 106-112
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Keywords

About this book

A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "The Geometry of Geodesics" (1955, quoted as G). It is the purpose of the present report to bring this theory up to date. Many of the later ip.vestigations were stimulated by problems posed in G, others concern newtopics. Naturally references to G are frequent. However, large parts, in particular Chapters I and III as weIl as several individual seetions, use only the basic definitions. These are repeated here, sometimes in a slightly different form, so as to apply to more general situations. In many cases a quoted result is quite familiar in Riemannian Geometry and consulting G will not be found necessary. There are two exceptions : The theory of paralleIs is used in Sections 13, 15 and 17 without reformulating all definitions and properties (of co-rays and limit spheres). Secondly, many items from the literature in G (pp. 409-412) are used here and it seemed superfluous to include them in the present list of references (pp. 106-110). The quotations are distinguished by [ ] and ( ), so that, for example, FreudenthaI [1] and (I) are found, respectively, in G and here.

Authors and Affiliations

  • University of Southern California, Los Angeles, USA

    Herbert Busemann

Bibliographic Information

  • Book Title: Recent Synthetic Differential Geometry

  • Authors: Herbert Busemann

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-88057-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1970

  • Softcover ISBN: 978-3-642-88059-9Published: 11 April 2012

  • eBook ISBN: 978-3-642-88057-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 112

  • Topics: Differential Geometry

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