Articles liés à Riemannian Geometry of Contact and Symplectic Manifolds
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Synopsis
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.
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Review
"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." a "Mathematical Reviews "Several examples accompany almost all chapters, in the first book in which the geometry of complex contract manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detale dand instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references. On the whole, this is a pleasant and useful book and all geometers will have a profit on reading it. They can use it for advanced courses, for thesis topics as well as for references. The beginners will find in it an attractive content and useful ideas for pursuing their studies." ---Memoriile Sectiilor Stiintifice
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