Hyperbolic geometry from a local viewpoint:
Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
|
| Schriftenreihe: | London Mathematical Society student texts
68 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems |
| Beschreibung: | 1 Online-Ressource (x, 271 Seiten) |
| ISBN: | 9780511618789 |
| DOI: | 10.1017/CBO9780511618789 |
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| 490 | 0 | |a London Mathematical Society student texts |v 68 | |
| 520 | |a Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems | ||
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Datensatz im Suchindex
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| author | Keen, Linda 1940- Lakic, Nikola 1966- |
| author_GND | (DE-588)140903763 (DE-588)14086749X |
| author_facet | Keen, Linda 1940- Lakic, Nikola 1966- |
| author_role | aut aut |
| author_sort | Keen, Linda 1940- |
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| bvnumber | BV043940793 |
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| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511618789 |
| format | Electronic eBook |
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| id | DE-604.BV043940793 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511618789 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349763 |
| oclc_num | 992926604 |
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| physical | 1 Online-Ressource (x, 271 Seiten) |
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| publishDate | 2007 |
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| publisher | Cambridge University Press |
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| spelling | Keen, Linda 1940- Verfasser (DE-588)140903763 aut Hyperbolic geometry from a local viewpoint Linda Keen, Nikola Lakic Cambridge Cambridge University Press 2007 1 Online-Ressource (x, 271 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 68 Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 Lakic, Nikola 1966- Verfasser (DE-588)14086749X aut Erscheint auch als Druck-Ausgabe 978-0-521-86360-5 Erscheint auch als Druck-Ausgabe 978-0-521-68224-4 https://doi.org/10.1017/CBO9780511618789 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Keen, Linda 1940- Lakic, Nikola 1966- Hyperbolic geometry from a local viewpoint Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Hyperbolic geometry from a local viewpoint |
| title_auth | Hyperbolic geometry from a local viewpoint |
| title_exact_search | Hyperbolic geometry from a local viewpoint |
| title_full | Hyperbolic geometry from a local viewpoint Linda Keen, Nikola Lakic |
| title_fullStr | Hyperbolic geometry from a local viewpoint Linda Keen, Nikola Lakic |
| title_full_unstemmed | Hyperbolic geometry from a local viewpoint Linda Keen, Nikola Lakic |
| title_short | Hyperbolic geometry from a local viewpoint |
| title_sort | hyperbolic geometry from a local viewpoint |
| topic | Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Geometry, Hyperbolic Hyperbolische Geometrie |
| url | https://doi.org/10.1017/CBO9780511618789 |
| work_keys_str_mv | AT keenlinda hyperbolicgeometryfromalocalviewpoint AT lakicnikola hyperbolicgeometryfromalocalviewpoint |