Anderson Hyperbolic Geometry

Erscheinungsjahr 2013
ISBN: 978-1-4471-3987-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 230 Seiten, Web PDF

Reihe: Springer Undergraduate Mathematics Series

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 new exercises.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Anderson, James W.

Inhaltsverzeichnis

1. The Basic Spaces.- 2. The General Möbius Group.- 3. Length and Distance in ?.- 4. Other Models of the Hyperbolic Plane.- 5. Convexity, Area, and Trigonometry.- 6. Groups Acting on ?.- Solutions.- Further Reading.- References.- Notation.