Progress in Mathematics Virtual Series on Symplectic Geometry

Riemannian Geometry of Contact and Symplectic Manifolds

Authors: Blair, David E.

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  • New material in most chapters
  • Major new topics are covered such as a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle
  • Improvements and general corrections based off of the first edition are made throughout
  • Intended for a broad audience of mathematicians, researchers, and students in Riemannian geometry
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  • ISBN 978-0-8176-4959-3
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About this book

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 reader.

Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics include a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of Étienne Ghys's attractive notion of a holomorphic Anosov flow.

Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite.

Reviews from the First Edition:

"The book . . . 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 sub-manifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics."   —Mathematical Reviews

"…this 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

Reviews

From the reviews:

"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

From the reviews of the second edition:

“In this book, contact and symplectic manifolds are studied from a Riemannian point of view … . The book is an excellent reference work for researchers interested in the Riemannian geometry of contact and symplectic manifolds as well as a very good introduction to the subject, containing a lot of examples. The number of examples has even increased compared to the first edition.” (Joeri Van der Veken, Mathematical Reviews, Issue 2012 d)


Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-0-8176-4959-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Geometry of Contact and Symplectic Manifolds
Authors
Series Title
Progress in Mathematics
Series Volume
203
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-0-8176-4959-3
DOI
10.1007/978-0-8176-4959-3
Hardcover ISBN
978-0-8176-4958-6
Series ISSN
0743-1643
Edition Number
2
Number of Pages
XV, 343
Number of Illustrations
8 b/w illustrations
Topics