Hyperbolic geometry, second revised edition

Anderson, J. W. (2005) Hyperbolic geometry, second revised edition (Springer Undergraduate Mathematics Series), London, UK. Springer London, 276pp.

Abstract

This is an undergraduate textbook covering the basics of planar hyperbolic geometry. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare 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; and many new exercises.

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Contributors

Author: J. W. Anderson

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