 Symplectic manifold

A symplectic manifold is an even-dimensional smooth manifold $M$ equipped with a closed nondegenerate differential two-form $\omega$.

A **symplectic manifold** is a smooth manifold \( M \) equipped with a closed non-degenerate differential 2-form called the **symplectic form**, typically denoted by \( \omega \). Formally, a symplectic manifold is defined as follows: 1. **Manifold**: \( M \) is a differentiable manifold of even dimension, usually denoted as \( 2n \), where \( n \) is a positive integer.