内容简介

This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space.It is divided into two closely related parts: the first treats the geometry of spaces of constant curvature and the second discrete groups of motions of these.The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian geometry and group theory.The result is a book which has no rival in the literature.
Part I contains the classification of motions in spaces of constant curvature and non-traditional topics like the theory of acute-angled polyhedra and methods for computing volumes of non-Euclidean polyhedra.Part II includes the theory of cristallographic, Fuchsian, and Kleinian groups and an exposition of Thurstonis theory of deformations.
The greater part of the book is accessible to first-year students in mathematics.At the same time the book includes very recent results which will be of interest to researchers in this field.