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Riemannian Geometry of Contact and Symplectic Manifolds

  • David E. Blair

Part of the Progress in Mathematics book series (PM, volume 203)

Table of contents

  1. Front Matter
    Pages i-xii
  2. David E. Blair
    Pages 1-10
  3. David E. Blair
    Pages 11-16
  4. David E. Blair
    Pages 17-29
  5. David E. Blair
    Pages 31-53
  6. David E. Blair
    Pages 63-89
  7. David E. Blair
    Pages 91-120
  8. David E. Blair
    Pages 121-135
  9. David E. Blair
    Pages 137-155
  10. David E. Blair
    Pages 177-187
  11. David E. Blair
    Pages 189-214
  12. David E. Blair
    Pages 215-225
  13. Back Matter
    Pages 227-260

About this book

Introduction

This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K"hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3-Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemannian geometric arena. The prerequisite for this text is a basic course in Riemannian geometry.

Keywords

Differential Geometry Differential Topology Manifolds Riemannian geometry curvature manifold

Authors and affiliations

  • David E. Blair
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3604-5
  • Copyright Information Birkhäuser Boston 2002
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3606-9
  • Online ISBN 978-1-4757-3604-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site