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Hyperbolic Geometry from a Local Viewpoint

Paperback / softback

Main Details

Title Hyperbolic Geometry from a Local Viewpoint
Authors and Contributors      By (author) Linda Keen
By (author) Nikola Lakic
SeriesLondon Mathematical Society Student Texts
Physical Properties
Format:Paperback / softback
Pages:282
Dimensions(mm): Height 229,Width 152
Category/GenreGeometry
ISBN/Barcode 9780521682244
ClassificationsDewey:516.9
Audience
Professional & Vocational
Illustrations Worked examples or Exercises; 5 Halftones, unspecified; 27 Line drawings, unspecified

Publishing Details

Publisher Cambridge University Press
Imprint Cambridge University Press
Publication Date 8 March 2007
Publication Country United Kingdom

Description

Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems.

Author Biography

Linda Keen is a Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center. Nikola Lakic is an Associate Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.

Reviews

'Here new and interesting results are collected and presented for a target audience of graduate students and researchers, but the first half of the book is well accessible also for undergraduate students, and indeed everyone who is interested in an introduction to hyperbolic geometry.' Internationale Mathematische Nachrichten