ENGLISH

Metric Spaces of Non-Positive Curvature

By André Haefliger (auth.) , Martin R. Bridson

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1999
ISBN
3540643249, 9783540643241
DOI
10.1007/978-3-662-12494-9
ISSN
0072-7830
LCC
QA611.28 .B75 1999
Open Library ID
OL43704M
Language
english
Format
DJVU
Filesize
7 MB (7484151 bytes)
Series
Grundlehren der mathematischen Wissenschaften 319
Edition
1
Pages
643\662
DPI
300
Scanned
no
Time added
2009-08-06 05:14:26
Manifolds and Cell Complexes (incl. Diff.Topology)

Description

The purpose of this book is to describe the global properties of complete simply­ connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .

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