Holdings: Hyperbolic Geometry

Hyperbolic Geometry:

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Bibliographic Details
Main Author:	Anderson, James W. 1964- (Author)
Format:	Electronic eBook
Language:	English
Published:	London [u.a.] Springer 2005
Edition:	2. ed.
Series:	Springer undergraduate mathematics series
Subjects:	Hyperbolische Geometrie
Online Access:	BTU01 TUM01 UBA01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource (XI, 276 S.) Ill., graph. Darst.
ISBN:	1852339349 9781846282201 9781852339340
DOI:	10.1007/1-84628-220-9

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MARC


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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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doi_str_mv	10.1007/1-84628-220-9
edition	2. ed.
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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
url	https://doi.org/10.1007/1-84628-220-9 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
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