Recall that a symplectic form on a 2n-dimensional manifold M is a closed 2-form Ω such that Ω n = Ω Λ Ω Λ ... Λ Ω (n times) is a volume form, i.e. a nowhere vanishing top dimensional differential form. The couple (M, Ω) is called a symplectic manifold, and the volume form Ω n is called the Liouvillie volume of the symplectic manifold (M, Ω).
KeywordsOpen Cover Symplectic Form Symplectic Manifold Lagrangian Submanifold Smooth Family
Unable to display preview. Download preview PDF.