Complex, Contact and Symmetric Manifolds In Honor of L. Vanhecke
This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contribu
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Series Editors Hyman Bass Joseph Oesterl´e Alan Weinstein
Complex, Contact and Symmetric Manifolds In Honor of L. Vanhecke
Old˘rich Kowalski Emilio Musso Domenico Perrone Editors
Birkh¨auser Boston • Basel • Berlin
Emilio Musso Universit`a di L’Aquila Dipartimento di Matematica Pura ed Applicata 67100 L’Aquila Italy
Old˘rich Kowalski Charles University Faculty of Mathematics and Physics 186 75 Praha Czech Republic Domenico Perrone Universit`a degli Studi di Lecce Dipartimento di Matematica “E. De Giorgi” 73100 Lecce Italy
AMS Subject Classifications: Primary: 53Cxx, 53Bxx, 53Dxx, 57Sxx, 58Kxx, 22Exx; Secondary: 53C15, 53C20, 53C21, 53C22, 53C25, 53C26, 53C30, 53C35, 53C40, 53C43, 53C50, 53C55, 53C65, 53B05, 53B20, 53B25, 53B30, 53B35, 53B40, 53D10, 53D15, 55S30, 55P62, 57S17, 57S25, 58K05, 22E15, 22E67
ISBN 0-8176-3850-4
Printed on acid-free paper.
c 2005 Birkh¨auser Boston
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media Inc., Rights and Permissions, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 987654321 www.birkhauser.com
SPIN 10944936
(TXQ/HP)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Curvature of Contact Metric Manifolds David E. Blair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
A Case for Curvature: the Unit Tangent Bundle H. Eric Boeckx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Convex Hypersurfaces in Hadamard Manifolds A. A. Borisenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Contact Metric Geometry of the Unit Tangent Sphere Bundle G. Calvaruso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
Topological–antitopological Fusion Equations, Pluriharmonic Maps and Special K¨ahler Manifolds Vicente Cort´es, Lars Sch¨afer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
Z2 and Z-Deformation Theory for Holomorphic and Symplectic Manifolds Paolo de Bartolomeis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension o
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