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This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.
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Differential Geometry Proceedings of the VIII International Colloquium 7219 tp.indd 1 4/1/09 8:31:36 AM This page intentionally left blank Differential Geometry Proceedings of the VIII International Colloquium Santiago de Compostela, Spain 7 – 11 July 2008 editors Jesús A Álvarez López Eduardo García-Río University of Santiago de Compostela, Spain World Scientific NEW JERSEY 7219 tp.indd 2 • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI 4/1/09 8:31:40 AM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Cover image: Self-portrait of Enrique Vidal Abascal DIFFERENTIAL GEOMETRY Proceedings of the VIII International Colloquium Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4261-16-6 ISBN-10 981-4261-16-5 Printed in Singapore. LaiFun - Differential Geometry.pmd 1 4/3/2009, 11:08 AM February 17, 2009 16:46 WSPC - Proceedings Trim Size: 9in x 6in viii-icdg v PREFACE This volume contains the papers contributed by the speakers of the VIII International Colloquium on Differential Geometry, which was held in Santiago de Compostela (Spain) during July 7–11, 2008. The Colloquium was organized by all members of the Department of Geometry and Topology of the University of Santiago de Compostela, and ´ M. Angeles de Prada of the University of Pa´ıs Vasco (Spain). The chairman ´ Cordero Rego. There were about 135 participants from many was Luis A. countries. We are most thankful to the following institutions that have cosponsored the Colloquium: the Department of Geometry and Topology, the Institute of Mathematics and the Faculty of Mathematics of the University of Santiago de Compostela, the “Ministerio de Educaci´ on y Ciencia” (projects MTM2006-01432 and MTM2007-30162-E), the “Ministerio de Ciencia y Tecnolog´ıa” (project MTM2008-02640), the “Conseller´ıa de Educaci´ on e Ordenaci´ on Universitaria da Xunta de Galicia”, the “Conseller´ıa de Innovaci´ on e Industria da Xunta de Galicia” (project PGIDIT06PXIB207054PR), and the “Consejo Superior de Investigaciones Cient´ıficas” of Spain. Their support was essential to carry out our program. The papers of this volume were mostly from the lectures presented at the Colloquium, which was designed with two main parts: Foliation Theory and Riemannian Geometry. All contributed papers were refereed, and we believe that they are of high quality, and make a significant progress on these subjects. Finally, we