Geometry II Spaces of Constant Curvature
Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to t
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Editor-in-Chief: R. V. Gamkrelidze
E. B. Vinberg (Ed.)
Geometry II Spaces of Constant Curvature
With 87 Figures
Springer-Verlag Berlin Heidelberg GmbH
Consulting Editors of the Series: A. A. Agrachev, A. A. Gonchar, E. F. Mishchenko, N.M.Ostianu, V. P. Sakharova, A.B.Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundarnental'nye napravleniya, Vol. 29, Geometriya 2 Publisher VINITI, Moscow 1988
Mathematics Subject Classification (1991): 20F55, 20Hxx, 51-:XX, 51F15, 51Mxx, 53Axx
ISBN 978-3-642-08086-9
Library of Congress Cataloging-in-Publication Data Geometriiii II. English. Geometry II: spaces of constant curvature I (ed.) E. B. Vinberg. p. em. - (Encyclopaedia of mathematical sciences; v. 29) Translation of: Geometriiii II, issued as v. 29 of the serial: Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamental 'nye napravleniiii . Includes bibliographical references and indexes. ISBN 978-3-642-08086-9 ISBN 978-3-662-02901-5 (eBook) DOI 10.1007/978-3-662-02901-5 1. Spaces of constant curvature. I. Vinberg, E. B. (Ernest Borisovich) II. Title. III. Title: Geometry 2. IV. Series. QA649.G46513 1993 516.3'63--dc20 92-31071 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. ©Springer-Verlag Berlin Heidelberg 1993 Originally published by Springer-Verlag Berlin Heidelberg New York in 1993 Softcover reprint of the hardcover I st edition 1993 Typesetting: Springer TEX in-house system 4113140-543210- Printed on acid-free paper
List of Editors, Authors and Translators Editor-in-Chifj R. V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia
Consulting Editor E. B. Vinberg, Department of Mathematics, Moscow University, 119899 Moscow, Russia
Authors D. V. Alekseevskij, Sophus Lie Centre, Krasnokazarmennaya 6, 111250 Moscow, Russia 0. V. Shvartsman, Department of Applied Mathematics, Moscow Institute of Communications, Aviamotomaya ul. Sa, 105855 Moscow, Russia A. S. Solodovnikov, State Financial Academy, 2nd Volkonskij per. 1, kv. 9, 103473 Moscow, Russia E. B. Vinberg, Department of Mathematics, Moscow University, 119899 Moscow, Russia
Translator V. Minachin, Cybernetics Council of the Russian Academy of Sciences, ul. Vavilova 40, 117966 Moscow, Russia
Contents I. Geometry of Spaces of Constant Curvature D. V. Alekseevskij, E. B. Vinberg, A. S. Solodov
