Riemannian Geometry of Contact and Symplectic Manifolds
Buch in deiner Nähe kaufen
Beschreibung
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.
The author's lectures, "Contact Manifolds in Riemannian Geometry," volume 509 (1976), in the Springer-Verlag Lecture Notes in Mathematics series have been out of print for some time and it seems appropriate that an expanded version of this material should become available. The present text deals with the Riemannian geometry of both symplectic and contact manifolds, although the book is more contact than symplectic. This work is based on the recent research of the author, his students, colleagues, and other scholars, the author's graduate courses at Michigan State University and the earlier lecture notes. Chapter 1 presents the general theory of symplectic manifolds. Principal circle bundles are then discussed in Chapter 2 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 Rie mannian metrics associated to symplectic and contact structures. Chapter 5 is devoted to integral submanifolds of the contact subbundle. In Chapter 6 we discuss the normality of almost contact structures, Sasakian manifolds, K contact manifolds, the relation of contact metric structures and CR-structures, and cosymplectic structures. Chapter 7 deals with the important study of the curvature of a contact metric manifold. In Chapter 8 we give a selection of results on submanifolds of Kahler and Sasakian manifolds, including an illus tration of the technique of A. Ros in a theorem of F. Urbano on compact minimal Lagrangian sub manifolds in cpn.
Monograph dealing with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. Carefully presented topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Main topics covered include: principal circle bundles, the general theory of contact manifolds, the general setting of Riemannian metrics associated with both symplectic and contact structures, integral submanifolds of the contact subbundle. Serves both as a general reference for mathematicians, and as an excellent resource for graduate students in the Riemannian geometric arena.
Autor*in
David E. Blair
Themen in »Riemannian Geometry of Contact and Symplectic Manifolds«
Differential Geometry Differential Topology Manifolds Riemannian geometry curvature manifold
Stimmen zu »Riemannian Geometry of Contact and Symplectic Manifolds«
"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
()