Locally Conformal Kahler Geometry

Progress in Mathematics Sorin Dragomir Liviu Ornea Locally Conformal Kahler Geometry Birkhauser Progress in Mathematics Volume 155 Series Editors Hyman Bass Joseph Oesterle Alan Weinstein Sorin Dragomir Liviu Ornea Locally Conformal Geometry Birkhauser Boston Basel Berlin Sorin Dragomir Dipartimento di Matematica University degli Studi della Basilicata 85100 Potenza, Italia Liviu Ornea Facultatea de Matmatica Universitatea din Bucuresti Bucure,§ti, Romania Library of Congress Cataloging-in-Publication Data Dragomir, Sorin, 1955Locally conformal Khhler geometry / Sorin Dragomir, Liviu Omea. cm. -- (Progress in mathematics ; v. 155) p. Includes bibliographical references. ISBN 0-8176-4020-7 -- ISBN 3-7643-4020-7 1. Khhlerian manifolds. 2. Geometry, Differential. I. Omea, II. Title. III. Series: Progress in mathematics Liviu, 1960. (Boston, Mass.) ; vol. 155 97-27397 QA649.D76 1997 CIP 515'.73--dc2l AMS Classification Codes: 53D20, 53C15, 53C40, 53C56. Printed on acid-free paper ® 1998 Birkhauser Birkhl user Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Birkhduser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be addressed directly to Birkhguser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. ISBN 0-8176-4020-7 ISBN 3-7643-4020-7 Reformatted from authors' disks by TsXniques, Inc. Boston, MA Printed and bound by Quinn-Woodbine, Woodbine, NJ Printed in the United States of America 987654321 Contents Introduction 1 ix L.c.K. Manifolds 1 2 Principally Important Properties 2.1 2.2 2.3 Vaisman's conjectures . Reducible manifolds Curvature properties . Blow-up . . . . . . . . . An adapted cohomology . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Examples 3.1 Hopf manifolds .. ... .. . . . . . . . . 3.2 7 . 7 10 . . 11 . . . . 15 16 . .. ... ...... . .. ... ...... . . 2.4 2.5 .. .. The Inoue surfaces .. . . . .. . . . . . . . ... . . . . . . . ........ .... . 3.3 A generalization of Thurston's manifold 3.4 A four-dimensional solvmanifold . . . . 3.5 SU(2) x S1 . .. 3.6 Noncompact examples . . . . . . . . . . 3.7 Brieskorn & Van de Ven's manifolds . . . . . . .