Metric Spaces of Non-Positive Curvature Hardback
by Martin R. Bridson, Andre Hafliger
Part of the Grundlehren der mathematischen Wissenschaften series
Hardback
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 .
Information
-
Out of stock
- Format:Hardback
- Pages:643 pages, XXI, 643 p.
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:15/10/1999
- Category:
- ISBN:9783540643241
Other Formats
- PDF from £101.58
Information
-
Out of stock
- Format:Hardback
- Pages:643 pages, XXI, 643 p.
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:15/10/1999
- Category:
- ISBN:9783540643241
