To set the stage for our development we begin this book with a treatment of the basic features of symplectic geometry. In this chapter we discuss symplectic 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.
KeywordsSymplectic Form Symplectic Manifold Betti Number Cotangent Bundle Ahler Manifold
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