Overview
- Thoroughly revised and updated
- Features new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity
- The only genuinely introductory textbook devoted to this topic: it is self-contained and assumes very few prerequisites
- Includes full solutions for all exercises – the only book on the subject to do so
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (6 chapters)
Keywords
About this book
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
This updated second edition also features:
- an expanded discussion of planar models of the hyperbolic plane arising from complex analysis;
- the hyperboloid model of the hyperbolic plane;
- a brief discussion of generalizations to higher dimensions;
- many newexercises.
Authors and Affiliations
Bibliographic Information
Book Title: Hyperbolic Geometry
Authors: James W. Anderson
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/1-84628-220-9
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2005
Softcover ISBN: 978-1-85233-934-0Published: 23 August 2005
eBook ISBN: 978-1-84628-220-1Published: 28 February 2006
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 2
Number of Pages: XII, 276
Number of Illustrations: 21 b/w illustrations
Topics: Geometry, Mathematics, general