RECENT SYNTHETIC DIFFERENTIAL GEOMETRY by Herbert Busemann ( 9783642880599 )

Item Details

Title:

RECENT SYNTHETIC DIFFERENTIAL GEOMETRY

By:

Format:

Paperback

List price:	£81.00
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ISBN 10:

3642880592

ISBN 13:

9783642880599

Publisher:

SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG

Pub. date:

11 April, 2012

Edition:

Softcover reprint of the original 1st ed. 1970

Series:

Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 54

Pages:

112

Synopsis:

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.

Illustrations:

VIII, 112 p.

Publication:

Germany

Imprint:

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Returns:

Returnable

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