Geometry II
Subtitle: spaces of constant curvature
By: E.B. Vinberg, (ed.).
Contributors: Vinberg, Ė. B.
Series: Encyclopaedia of mathematical sciences ;; v. 29
Publisher: Springer-Verlag
Published: 1993
Place of publication: Berlin; New York
Language: eng
Number of pages: 254
Subjects: Spaces of constant curvature
Other titles: Geometry 2.
Description: 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. 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 Thurston's 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.
Notes: Includes bibliographical references and indexes.
Translation of: Geometrii͡a︡ II, issued as v. 29 of the serial: Itogi nauki i tekhniki. Sovremennye problemy matermatiki. Fundamentalʹnye napravlenii͡a︡.