Titlebook: Riemannian Geometry of Contact and Symplectic Manifolds; David E. Blair Book 2010Latest edition Springer Science+Business Media LLC 2010 D

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https://doi.org/10.1007/978-0-8176-4959-3Differential Geometry; Differential Topology; Manifolds; Riemannian geometry; curvature; manifold; symplec

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Contact Manifolds,In this chapter we give the basic definitions and properties concerning contact manifolds both as given by a global contact form and as a contact structure in the wider sense. We then give many examples of contact manifolds, a discussion of the celebrated Boothby–Wang fibration, and a discussion of the Weinstein conjecture.

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Curvature of Contact Metric Manifolds,In this chapter we discuss many aspects of the curvature of contact metric manifolds. As such, it is to be regarded as one of the most important chapters in this book.

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,Submanifolds of Kähler and Sasakian Manifolds,In this chapter we study submanifolds in both contact and Kähler geometry. These are extensive subjects in their own right, and we give only a few basic results.

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Complex Contact Manifolds,While the study of complex contact manifolds is almost as old as the modern theory of real contact manifolds, the subject has received much less attention, and since many examples are now appearing in the literature, we devote this and the next chapter to the subject.

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3-Sasakian Manifolds,In this chapter we will give more of a survey of 3-Sasakian manifolds and only a few proofs. A more thorough treatment is given in the book by Boyer and Galicki [2008, Chapter 13].

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Symplectic Manifolds,lectic manifolds and make brief mention of “associated metrics”, a topic that will be thoroughly discussed in Chapter 4. Here we treat in detail Lagrangian submanifolds and theorems of Darboux and Weinstein on the local structure of a symplectic manifold. We end this chapter with a brief discussion of symplectomorphisms.