Hermitian Spaces
Affine complex spaces can be provided with an “Hermitian product” which yields corresponding notions of distance and perpendicularity. The similarities and differences with the Euclidean case are clearly underlined.
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An Algebraic Approach to Geometry Geometric Trilogy II
An Algebraic Approach to Geometry
Francis Borceux
An Algebraic Approach to Geometry Geometric Trilogy II
Francis Borceux Université catholique de Louvain Louvain-la-Neuve, Belgium
ISBN 978-3-319-01732-7 ISBN 978-3-319-01733-4 (eBook) DOI 10.1007/978-3-319-01733-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013953917 Mathematics Subject Classification (2010): 51N10, 51N15, 51N20, 51N35 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover image: René Descartes, etching 1890 after a painting by Frans Hals, artist unknown Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To François, Sébastien, Frédéric, Rachel, Emmanuel and Ludovic
Preface
The reader is invited to immerse himself in a “love story” which has been unfolding for 35 centuries: the love story between mathematicians and geometry. In addition to accompanying the reader up to the present state of the art, the purpose of this Trilogy is precisely to tell this story. The Geometric Trilogy will introduce the reader to the multiple complementary aspects of geometry, first paying tribute to the historical work on which it is based, and then switching to a more contemporary treatment, making full use o
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