Metric Spaces of Non-Positive Curvature:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1999
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
319 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XXI, 643 p) |
| ISBN: | 9783662124949 9783642083990 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-12494-9 |
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Datensatz im Suchindex
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-12494-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423472 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662124949 9783642083990 |
| issn | 0072-7830 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Bridson, Martin R. Verfasser aut Metric Spaces of Non-Positive Curvature by Martin R. Bridson, André Haefliger Berlin, Heidelberg Springer Berlin Heidelberg 1999 1 Online-Ressource (XXI, 643 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 319 0072-7830 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 Mathematics Group theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Group Theory and Generalizations Mathematik Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Nichtpositive Krümmung (DE-588)4128763-0 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s Nichtpositive Krümmung (DE-588)4128763-0 s 1\p DE-604 Haefliger, André Sonstige oth https://doi.org/10.1007/978-3-662-12494-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bridson, Martin R. Metric Spaces of Non-Positive Curvature Mathematics Group theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Group Theory and Generalizations Mathematik Metrischer Raum (DE-588)4169745-5 gnd Nichtpositive Krümmung (DE-588)4128763-0 gnd |
| subject_GND | (DE-588)4169745-5 (DE-588)4128763-0 |
| title | Metric Spaces of Non-Positive Curvature |
| title_auth | Metric Spaces of Non-Positive Curvature |
| title_exact_search | Metric Spaces of Non-Positive Curvature |
| title_full | Metric Spaces of Non-Positive Curvature by Martin R. Bridson, André Haefliger |
| title_fullStr | Metric Spaces of Non-Positive Curvature by Martin R. Bridson, André Haefliger |
| title_full_unstemmed | Metric Spaces of Non-Positive Curvature by Martin R. Bridson, André Haefliger |
| title_short | Metric Spaces of Non-Positive Curvature |
| title_sort | metric spaces of non positive curvature |
| topic | Mathematics Group theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Group Theory and Generalizations Mathematik Metrischer Raum (DE-588)4169745-5 gnd Nichtpositive Krümmung (DE-588)4128763-0 gnd |
| topic_facet | Mathematics Group theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Group Theory and Generalizations Mathematik Metrischer Raum Nichtpositive Krümmung |
| url | https://doi.org/10.1007/978-3-662-12494-9 |
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