Riemannian Geometry of Contact and Symplectic Manifolds
This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the
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Series Editors Hyman Bass Joseph Oesterlé Alan Weinstein
David E. Blair
Riemannian Geometry of Contact and Symplectic Manifolds Second Edition
David E. Blair Department of Mathematics Michigan State University East Lansing, MI 48824-1027 USA [email protected]
ISBN 978-0-8176-4958-6 e-ISBN 978-0-8176-4959-3 DOI 10.1007/978-0-8176-4959-3 Library of Congress Control Number: 2010932450 Mathematics Subject Classification (2010): 53B35, 53C15, 53C25, 53C26, 53C40, 53C42, 53C55, 53C56, 53D05, 53D10, 53D12, 53D15, 53D22, 53D25, 53D35, 58E11 © Springer Science+Business Media, LLC 2002, 2010 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, LLC, 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 on acid-free paper birkhauser-science.com
To Rebecca in appreciation of all her love and support
Preface to Second Edition
For this second edition almost every chapter has been revised and updated in some way. The principal changes from the first edition are the following. A second chapter on the geometry of complex contact manifolds, Chapter 13, has been added. Chapter 7 on the curvature of contact metric manifolds has been reorganized and updated extensively. A section on the projectivized tangent bundle has been added to Chapter 9. Additional examples and commentary on further results have been added throughout. There has been considerable work in recent years on a number of areas related to the subject, and it has been impossible to treat all of this work. The author believes, however, that the text offers a good introduction to and necessary background for the study of these topics. The author expresses his appreciation to C. Abbas, T. Draghici, B. Foreman and B. Korkmaz for reading parts of the manuscript and offering valuable suggestions. The author also expresses his appreciation to Birkh¨ auser for suggesting that he write a second edition and especially to Ann Kostant, Jessica Belanger and Tom Grasso for their kind assistance in producing this book. March, 2010
David E. Blair vii
Preface to the First Edition
The author’s lectures “Contact Manifolds in Riemannian Geometry”, volume 509 (1976), in the Springer-Verlag series Lecture Notes in Mathematics have been out of print for some time and it seems appropriate that an expanded version of this material should become available. The present text deals with the Riemannian geometry of both symplectic and contact manifolds, although the book is mor
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