Lectures on Spaces of Nonpositive Curvature:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1995
|
| Schriftenreihe: | DMV Seminars
25 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory |
| Beschreibung: | 1 Online-Ressource (120p) |
| ISBN: | 9783034892407 9783764352424 |
| DOI: | 10.1007/978-3-0348-9240-7 |
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| 500 | |a Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory | ||
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Datensatz im Suchindex
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| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9240-7 |
| format | Electronic eBook |
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| isbn | 9783034892407 9783764352424 |
| language | English |
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| spelling | Ballmann, Werner Verfasser aut Lectures on Spaces of Nonpositive Curvature by Werner Ballmann Basel Birkhäuser Basel 1995 1 Online-Ressource (120p) txt rdacontent c rdamedia cr rdacarrier DMV Seminars 25 Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory Mathematics Group theory Topological Groups Global analysis (Mathematics) Global differential geometry Algebraic topology Cell aggregation / Mathematics Differential Geometry Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s Nichtpositive Krümmung (DE-588)4128763-0 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-9240-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ballmann, Werner Lectures on Spaces of Nonpositive Curvature Mathematics Group theory Topological Groups Global analysis (Mathematics) Global differential geometry Algebraic topology Cell aggregation / Mathematics Differential Geometry Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4128763-0 (DE-588)4169745-5 |
| title | Lectures on Spaces of Nonpositive Curvature |
| title_auth | Lectures on Spaces of Nonpositive Curvature |
| title_exact_search | Lectures on Spaces of Nonpositive Curvature |
| title_full | Lectures on Spaces of Nonpositive Curvature by Werner Ballmann |
| title_fullStr | Lectures on Spaces of Nonpositive Curvature by Werner Ballmann |
| title_full_unstemmed | Lectures on Spaces of Nonpositive Curvature by Werner Ballmann |
| title_short | Lectures on Spaces of Nonpositive Curvature |
| title_sort | lectures on spaces of nonpositive curvature |
| topic | Mathematics Group theory Topological Groups Global analysis (Mathematics) Global differential geometry Algebraic topology Cell aggregation / Mathematics Differential Geometry Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Mathematik Nichtpositive Krümmung (DE-588)4128763-0 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Mathematics Group theory Topological Groups Global analysis (Mathematics) Global differential geometry Algebraic topology Cell aggregation / Mathematics Differential Geometry Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Mathematik Nichtpositive Krümmung Metrischer Raum |
| url | https://doi.org/10.1007/978-3-0348-9240-7 |
| work_keys_str_mv | AT ballmannwerner lecturesonspacesofnonpositivecurvature |