Symplectic Manifolds

Abstract

To set the stage for our development, we begin this book with a treatment of the basic features of symplectic geometry. By a symplectic manifold we mean an even-dimensional differentiable (C ^∞) manifold M ²ⁿ n together with a global 2-form Ω which is closed and of maximal rank, i.e., dΩ = 0, Ω ⁿ ≠ 0. By a symplectomorphism f: (M ₁, Ω₁) → (M ₂, Ω₂) we mean a diffeomorphism f : M ₁ → M ₂ such that f*Ω₂ =Ω₁.