Recent Synthetic Differential Geometry by Herbert Busemann
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Recent Synthetic Differential Geometry

Recent Synthetic Differential Geometry


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About the 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.


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Product Details
  • ISBN-13: 9783642880599
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 112
  • Series Title: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge
  • Weight: 236 gr
  • ISBN-10: 3642880592
  • Publisher Date: 11 Apr 2012
  • Edition: Softcover reprint of the original 1st ed. 1970
  • Language: English
  • Returnable: Y
  • Spine Width: 7 mm
  • Width: 156 mm


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