Classical Geometries in Modern Contexts Geometry of Real Inner Product Spaces 3764373717.pdf

Classical
Geometries in
Modern
Walter Benz Contexts
Geometry of Real Inner
Product Spaces
Birkhäuser Verlag
Basel • Boston • Berlin
Authors:
Walter Benz
Fachbereich Mathematik
Universität Hamburg
Bundesstr. 55
20146 Hamburg
Germany
e-mail: ******@-
2000 Mathematical Subject Classification 39B52, 51B10, 51B25, 51M05, 51M10, 83C20
A CIP catalogue record for this book is available from the
Library of Congress, Washington ., USA
Bibliographic information published by Die Deutsche Bibliothek
Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data is available in the at <>.
ISBN 3-7643-7371-7 Birkhäuser Verlag, Basel – Boston – Berlin
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, re-use of illustrations, recitation, broadcast-
ing, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use
permission of the copyright owner must be obtained.
© 2005 Birkhäuser Verlag, . Box 133, CH-4010 Basel, Switzerland
Part of Springer Science+Business Media
Cover design: Micha Lotrovsky, CH-4106 Therwil, Switzerland
Printed on acid-free paper produced from chlorine-free pulp. TCF °°
Printed in Germany
ISBN-10: 3-7643-7371-7 e-ISBN: 3-7643-7432-2
ISBN-13: 978-3-7643-7371-9
9 8 7 6 5 4 3 2 1
Contents
Preface ix
1 Translation Groups 1
....................... 1
................................ 2
Isomorphic, non-isomorphic spaces . . . . . . . . . . . . . . . . . . 3
–Schwarz..................... 4
Orthogonal mappings . . . . . . . . . . . . . . . . . . . . . . . . . 5
A characterization of orthogonal mappings . . . . . . . . . . . . . . 7
,axis,kernel.................... 10