Riemannian Geometry of Contact and Symplectic Manifolds - (Progress in Mathematics) 2nd Edition by David E Blair (Hardcover)
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<p/><br></br><p><b> About the Book </b></p></br></br><p>This second edition 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.</p><p/><br></br><p><b> Book Synopsis </b></p></br></br>Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kähler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index<p/><br></br><p><b> From the Back Cover </b></p></br></br><p>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.</p> <p><em>Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition</em> 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.</p> <p>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.</p> <p><strong>Reviews from the First Edition: </strong></p> <p><em>"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." </em><strong>--Mathematical Reviews</strong></p> <p><em>"...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." </em><strong>--Memoriile Sectiilor Stiintifice</strong></p><p/><br></br><p><b> Review Quotes </b></p></br></br><br>From the reviews: <p>"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." <b>--Mathematical Reviews</b></p><p>"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." <b>--Memoriile Sectiilor Stiintifice</b></p><p>From the reviews of the second edition: </p><p>"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)</p><br>
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