Every cotangent bundle T*M has a canonical 1-form θ (Liouville/tautological form) whose exterior derivative ω = dθ is the canonical symplectic form. Darboux's theorem says every symplectic manifold is locally modelled on (T*ℝⁿ, dθ).
Every cotangent bundle T*M has a canonical 1-form θ (Liouville/tautological form) whose exterior derivative ω = dθ is the canonical symplectic form. Darboux's theorem says every symplectic manifold is locally modelled on (T*ℝⁿ, dθ).