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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, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations.
Topics covered include the upper half-plane model of the hyperbolic plane, Mbius transformations, the general Mbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincar disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula 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;
brief discussion of generalizations to higher dimensions;
many new exercises.
The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape.
Details
- Title Hyperbolic Geometry
- Author James W. Anderson
- Binding Paperback
- Edition 2nd
- Pages 276
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2005-08-23
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- ISBN 9781852339340 / 1852339349
- Weight 1.1 lbs (0.50 kg)
- Dimensions 9.9 x 6.9 x 0.7 in (25.15 x 17.53 x 1.78 cm)
- Library of Congress Catalog Number 2005923338
- Dewey Decimal Code 516.9
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