Skew Curves
Curves in the three dimensional real space are studied from the points of view of their equations, their tangent, their curvature and their torsion. We establish the Frenet formulas and we investigate the more involved question of the intrinsic equations
- PDF / 25,254,878 Bytes
- 462 Pages / 441 x 666 pts Page_size
- 1 Downloads / 198 Views
A Differential Approach to Geometry Geometric Trilogy III
A Differential Approach to Geometry
Francis Borceux
A Differential Approach to Geometry Geometric Trilogy III
Francis Borceux Université catholique de Louvain Louvain-la-Neuve, Belgium
ISBN 978-3-319-01735-8 ISBN 978-3-319-01736-5 (eBook) DOI 10.1007/978-3-319-01736-5 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013954709 Mathematics Subject Classification (2010): 53A04, 53A05, 53A45, 53A55, 53B20, 53C22, 53C45 © 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: Carl Friedrich Gauss by Christian Albrecht Jensen Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Océane, Anaïs, Magali, Lucas, Cyprien, Théophile, Constance, Léonard, Georges, . . . and those still to come
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 t
