This introductory text explores and develops the basic notions of geometry on the hyperbolic plane. 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 Poincar disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. Coverage provides readers with a firm grasp of the concepts and techniques of this beautiful area of mathematics.

Klappentext

Thoroughly updated, featuring new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity

Includes full solutions for all exercises

Successful first edition sold over 800 copies in North America

Inhalt

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.