Recent Synthetic Differential Geometry

  • Herbert┬áBusemann

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

Table of contents

  1. Front Matter
    Pages I-VII
  2. Herbert Busemann
    Pages 27-40
  3. Herbert Busemann
    Pages 41-55
  4. Herbert Busemann
    Pages 56-90
  5. Herbert Busemann
    Pages 91-100
  6. Herbert Busemann
    Pages 101-105
  7. Back Matter
    Pages 106-112

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.


Differentialgeometrie Riemannian geometry Synthetic Differential Geometry differential geometry geometry

Authors and affiliations

  • Herbert┬áBusemann
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1970
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88059-9
  • Online ISBN 978-3-642-88057-5
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site