Geometry of Hypersurfaces
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfac
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Thomas E. Cecil Patrick J. Ryan
Geometry of Hypersurfaces
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Thomas E. Cecil • Patrick J. Ryan
Geometry of Hypersurfaces
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Thomas E. Cecil Department of Mathematics and Computer Science College of the Holy Cross Worcester, MA, USA
Patrick J. Ryan Department of Mathematics and Statistics McMaster University Hamilton, ON, Canada
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-1-4939-3245-0 ISBN 978-1-4939-3246-7 (eBook) DOI 10.1007/978-1-4939-3246-7 Library of Congress Control Number: 2015947495 Mathematics Subject Classification (2010): 53B25, 53C40, 53C42 Springer New York Heidelberg Dordrecht London © Thomas E. Cecil and Patrick J. Ryan 2015 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com)
To our wives, Patsy and Ellen
Preface
The purpose of this book is to provide a thorough, up-to-date treatment of the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms and Hopf hypersurfaces in complex space forms. An indepth discussion of these topics and the contents of each chapter is given in the introduction. The presentation is aimed at a reader who has completed a one-year graduate course in differential geometry and manifold theory. This book could be used for a second graduate course in differential geometry, a research seminar or as a reference. The material in Chapters 2 and 3 has substantial overlap with our book Tight and Taut Immersions of Manifolds [95], published in 1985. For many topics, the order of the presentation has been changed significantly from our earlier book, and the material has been updated to include results published after 1985. Chapter 4 cont
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