Nonpositive Curvature: Geometric and Analytic Aspects:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1997
|
| Schriftenreihe: | Lectures in Mathematics ETH Zürich, Department of Mathematics Research Institute of Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The present book contains the lecture notes from a "Nachdiplomvorlesung", a topics course adressed to Ph. D. students, at the ETH ZUrich during the winter term 95/96. Consequently, these notes are arranged according to the requirements of organizing the material for oral exposition, and the level of difficulty and the exposition were adjusted to the audience in Zurich. The aim of the course was to introduce some geometric and analytic concepts that have been found useful in advancing our understanding of spaces of nonpos itive curvature. In particular in recent years, it has been realized that often it is useful for a systematic understanding not to restrict the attention to Riemannian manifolds only, but to consider more general classes of metric spaces of generalized nonpositive curvature. The basic idea is to isolate a property that on one hand can be formulated solely in terms of the distance function and on the other hand is characteristic of nonpositive sectional curvature on a Riemannian manifold, and then to take this property as an axiom for defining a metric space of nonpositive curvature. Such constructions have been put forward by Wald, Alexandrov, Busemann, and others, and they will be systematically explored in Chapter 2. Our focus and treatment will often be different from the existing literature. In the first Chapter, we consider several classes of examples of Riemannian manifolds of nonpositive curvature, and we explain how conditions about nonpositivity or negativity of curvature can be exploited in various geometric contexts |
| Beschreibung: | 1 Online-Ressource (VIII, 112 p.) 3 illus |
| ISBN: | 9783034889186 9783764357368 |
| DOI: | 10.1007/978-3-0348-8918-6 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8918-6 |
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| institution | BVB |
| isbn | 9783034889186 9783764357368 |
| language | English |
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| series2 | Lectures in Mathematics ETH Zürich, Department of Mathematics Research Institute of Mathematics |
| spelling | Jost, Jürgen Verfasser aut Nonpositive Curvature: Geometric and Analytic Aspects by Jürgen Jost Basel Birkhäuser Basel 1997 1 Online-Ressource (VIII, 112 p.) 3 illus txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics ETH Zürich, Department of Mathematics Research Institute of Mathematics The present book contains the lecture notes from a "Nachdiplomvorlesung", a topics course adressed to Ph. D. students, at the ETH ZUrich during the winter term 95/96. Consequently, these notes are arranged according to the requirements of organizing the material for oral exposition, and the level of difficulty and the exposition were adjusted to the audience in Zurich. The aim of the course was to introduce some geometric and analytic concepts that have been found useful in advancing our understanding of spaces of nonpos itive curvature. In particular in recent years, it has been realized that often it is useful for a systematic understanding not to restrict the attention to Riemannian manifolds only, but to consider more general classes of metric spaces of generalized nonpositive curvature. The basic idea is to isolate a property that on one hand can be formulated solely in terms of the distance function and on the other hand is characteristic of nonpositive sectional curvature on a Riemannian manifold, and then to take this property as an axiom for defining a metric space of nonpositive curvature. Such constructions have been put forward by Wald, Alexandrov, Busemann, and others, and they will be systematically explored in Chapter 2. Our focus and treatment will often be different from the existing literature. In the first Chapter, we consider several classes of examples of Riemannian manifolds of nonpositive curvature, and we explain how conditions about nonpositivity or negativity of curvature can be exploited in various geometric contexts Mathematics Global differential geometry Differential Geometry Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 s Nichtpositive Krümmung (DE-588)4128763-0 s 1\p DE-604 Metrischer Raum (DE-588)4169745-5 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-8918-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jost, Jürgen Nonpositive Curvature: Geometric and Analytic Aspects Mathematics Global differential geometry Differential Geometry Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd Riemannscher Raum (DE-588)4128295-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4128763-0 (DE-588)4128295-4 (DE-588)4169745-5 |
| title | Nonpositive Curvature: Geometric and Analytic Aspects |
| title_auth | Nonpositive Curvature: Geometric and Analytic Aspects |
| title_exact_search | Nonpositive Curvature: Geometric and Analytic Aspects |
| title_full | Nonpositive Curvature: Geometric and Analytic Aspects by Jürgen Jost |
| title_fullStr | Nonpositive Curvature: Geometric and Analytic Aspects by Jürgen Jost |
| title_full_unstemmed | Nonpositive Curvature: Geometric and Analytic Aspects by Jürgen Jost |
| title_short | Nonpositive Curvature: Geometric and Analytic Aspects |
| title_sort | nonpositive curvature geometric and analytic aspects |
| topic | Mathematics Global differential geometry Differential Geometry Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd Riemannscher Raum (DE-588)4128295-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Mathematics Global differential geometry Differential Geometry Mathematik Nichtpositive Krümmung Riemannscher Raum Metrischer Raum |
| url | https://doi.org/10.1007/978-3-0348-8918-6 |
| work_keys_str_mv | AT jostjurgen nonpositivecurvaturegeometricandanalyticaspects |