© 2002

Riemannian Geometry of Contact and Symplectic Manifolds


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


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.


Differential Geometry Differential Topology Manifolds Riemannian geometry curvature manifold

Authors and affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Bibliographic information

  • Book Title Riemannian Geometry of Contact and Symplectic Manifolds
  • Authors David E. Blair
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Boston 2002
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4261-7
  • Softcover ISBN 978-1-4757-3606-9
  • eBook ISBN 978-1-4757-3604-5
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XII, 260
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Manifolds and Cell Complexes (incl. Diff.Topology)
  • Buy this book on publisher's site


"The book . . . supplies a lot of examples, and includes many recent results. It can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics."   —Mathematical Reviews

"Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive [table of] contents and useful ideas for pursuing their studies."   —Memoriile Sectiilor Stiintifice