Hyperbolic Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2005
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource (XI, 276 S.) Ill., graph. Darst. |
| ISBN: | 1852339349 9781846282201 9781852339340 |
| DOI: | 10.1007/1-84628-220-9 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804136322028273664 |
|---|---|
| adam_text | Contents
Preamble to the Second Edition vii
Preamble to the First Edition ix
1. The Basic Spaces 1
1.1 A Model for the Hyperbolic Plane 1
1.2 The Riemann Sphere C 8
1.3 The Boundary at Infinity of H 18
2. The General Mobius Group 23
2.1 The Group of Mobius Transformations 23
2.2 Transitivity Properties of Mob+ 30
2.3 The Cross Ratio 36
2.4 Classification of Mobius Transformations 39
2.5 A Matrix Representation 42
2.6 Reflections 48
2.7 The Conformality of Elements of Mob 53
2.8 Preserving H 56
2.9 Transitivity Properties of M6b(H) 62
2.10 The Geometry of the Action of M6b(H) 65
v
3. Length and Distance in H 73
3.1 Paths and Elements of Arc length 73
3.2 The Element of Arc length on H 80
3.3 Path Metric Spaces 88
3.4 From Arc length to Metric 92
3.5 Formulae for Hyperbolic Distance in HI 99
3.6 Isometries 103
3.7 Metric Properties of (H, dH) 108
4. Planar Models of the Hyperbolic Plane 117
4.1 The Poincare Disc Model 117
4.2 A General Construction 130
5. Convexity, Area, and Trigonometry 145
5.1 Convexity 145
5.2 Hyperbolic Polygons 154
5.3 The Definition of Hyperbolic Area 164
5.4 Area and the Gauss Bonnet Formula 169
5.5 Applications of the Gauss Bonnet Formula 174
5.6 Trigonometry in the Hyperbolic Plane 181
6. Nonplanar models 189
6.1 The Hyperboloid Model of the Hyperbolic Plane 189
6.2 Higher Dimensional Hyperbolic Spaces 209
Solutions to Exercises 217
References 265
List of Notation 269
Index 273
|
| adam_txt |
Contents
Preamble to the Second Edition vii
Preamble to the First Edition ix
1. The Basic Spaces 1
1.1 A Model for the Hyperbolic Plane 1
1.2 The Riemann Sphere C 8
1.3 The Boundary at Infinity of H 18
2. The General Mobius Group 23
2.1 The Group of Mobius Transformations 23
2.2 Transitivity Properties of Mob+ 30
2.3 The Cross Ratio 36
2.4 Classification of Mobius Transformations 39
2.5 A Matrix Representation 42
2.6 Reflections 48
2.7 The Conformality of Elements of Mob 53
2.8 Preserving H 56
2.9 Transitivity Properties of M6b(H) 62
2.10 The Geometry of the Action of M6b(H) 65
v
3. Length and Distance in H 73
3.1 Paths and Elements of Arc length 73
3.2 The Element of Arc length on H 80
3.3 Path Metric Spaces 88
3.4 From Arc length to Metric 92
3.5 Formulae for Hyperbolic Distance in HI 99
3.6 Isometries 103
3.7 Metric Properties of (H, dH) 108
4. Planar Models of the Hyperbolic Plane 117
4.1 The Poincare Disc Model 117
4.2 A General Construction 130
5. Convexity, Area, and Trigonometry 145
5.1 Convexity 145
5.2 Hyperbolic Polygons 154
5.3 The Definition of Hyperbolic Area 164
5.4 Area and the Gauss Bonnet Formula 169
5.5 Applications of the Gauss Bonnet Formula 174
5.6 Trigonometry in the Hyperbolic Plane 181
6. Nonplanar models 189
6.1 The Hyperboloid Model of the Hyperbolic Plane 189
6.2 Higher Dimensional Hyperbolic Spaces 209
Solutions to Exercises 217
References 265
List of Notation 269
Index 273 |
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| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1007/1-84628-220-9 |
| edition | 2. ed. |
| format | Electronic eBook |
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| isbn | 1852339349 9781846282201 9781852339340 |
| language | English |
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| spelling | Anderson, James W. 1964- Verfasser (DE-588)121142450 aut Hyperbolic Geometry James W. Anderson 2. ed. London [u.a.] Springer 2005 1 Online-Ressource (XI, 276 S.) Ill., graph. Darst. txt rdacontent c rdamedia cr rdacarrier Springer undergraduate mathematics series Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s b DE-604 https://doi.org/10.1007/1-84628-220-9 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015513379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anderson, James W. 1964- Hyperbolic Geometry Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Hyperbolic Geometry |
| title_auth | Hyperbolic Geometry |
| title_exact_search | Hyperbolic Geometry |
| title_exact_search_txtP | Hyperbolic Geometry |
| title_full | Hyperbolic Geometry James W. Anderson |
| title_fullStr | Hyperbolic Geometry James W. Anderson |
| title_full_unstemmed | Hyperbolic Geometry James W. Anderson |
| title_short | Hyperbolic Geometry |
| title_sort | hyperbolic geometry |
| topic | Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Hyperbolische Geometrie |
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