Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

Recent Synthetic Differential Geometry

Authors: Busemann, Herbert

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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.

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Buy this book

eBook $99.00 net
( price for USA )
  • ISBN 978-3-642-88057-5
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $129.00 net
( price for USA )
  • ISBN 978-3-642-88059-9
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Recent Synthetic Differential Geometry
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Series Volume
54
Copyright
1970
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-88057-5
DOI
10.1007/978-3-642-88057-5
Softcover ISBN
978-3-642-88059-9
Edition Number
1
Topics