Hyperbolic geometry, (Undergraduate math ematics series), (2nd Ed.)

Author:

Language: Anglais
Cover of the book Hyperbolic geometry, (Undergraduate math ematics series),

Subject for Hyperbolic geometry, (Undergraduate math ematics series),

47.46 €

In Print (Delivery period: 15 days).

Add to cartAdd to cart
Publication date:
Support: Imprimé à la demande
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.
Preamble to the Second Edition
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.