Riemannian Geometry of Contact and Symplectic Manifolds

The author s lectures Contact Manifolds in Riemannian Geometry, volume 509 (1976), in the Springer-Verlag series Lecture Notes in Mathematics have beenout of print for sometime and it seems approp- ate that an expanded version of this material should become available. Thepresenttext deals withtheRie [...]
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The author s lectures Contact Manifolds in Riemannian Geometry, volume 509 (1976), in the Springer-Verlag series Lecture Notes in Mathematics have beenout of print for sometime and it seems approp- ate that an expanded version of this material should become available. Thepresenttext deals withtheRiemannian geometry of bothsymplectic and contact manifolds, although the book is more contact than sympl- tic. This work is based on the recent research of the author, his students, colleagues, andotherscholars, theauthor sgraduatecoursesat Michigan State University and the earlier lecture notes. Chapter 1 presents the general theory of symplectic manifolds. Pr- cipal circle bundles are then discussed in Chapter 2 as a prelude to the Boothby Wang ?bration of a compact regular contact manifold in Ch- ter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on Riemannian metrics associated to symplectic and contact structures. Chapter 5 is devoted to integral submanifolds of the contact subbundle. InChapter6wediscussthenormalityofalmostcontactstr- tures, Sasakian manifolds, K-contact manifolds, the relation of contact metricstructures andCR-structures, andcosymplectic structures. Ch- ter 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 ix x Preface to the First Edition K] ahler andSasakian manifolds, includingan illustration of thetechnique of A. Ros in a theorem of F. Urbano on compact minimal Lagrangian n submanifolds in CP ."