Hyperbolic Geometry. Springer Undergraduate Mathematics Series (SUMS)

Seitenzahl:

276

Gewicht:

562 g

Auflage:

2nd ed.

Erschienen bei:

Springer Verlag GmbH

Kurzbeschreibung

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. TOC:Preamble to the Second Edition
Preamble to the First Edition
The Basic Spaces
The General Möbius Group
Length and Distance in H
Planar Models of the Hyperbolic Plane
Convexity, Area and Trigonometry
Non-planar models
Solutions to Exercises
References; List of Notation
Index

Beschreibung

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.

Inhaltsverzeichnis

Contents:§Preamble§The Basic Spaces§The General Möbius Group§Length and Distance in H§Other Models of the Hyperbolic Plane§Convexity, Area and Trigonometry. Groups Acting on H§Solutions§Further Reading§References§Notation§Index

Mehr über...

Mehr über:  Mathematics, Nichteuklidische Geometrie, Geometry, Hyperbolic geometry, Hyperbolic plane, Hyperbolicity, Mathematics / Geometry / Non-Euclidean

Mehr von: 

Mehr von:  James W. Anderson, Springer Verlag GmbH