Closed, non-degenerate 2-form ω on a 2n-manifold: dω = 0 and ω^n ≠ 0 pointwise. Non-degeneracy makes T_pM → T_p*M, v ↦ ι_v ω an isomorphism, supplying the canonical Poisson bracket on C^∞(M).
Symplectic form
Related concepts
- Differential form
- Smooth manifold
- Symplectic manifold
- Darboux theorem
- Hamiltonian vector field
- Poisson bracket
- Lagrangian submanifold
- Moment map
- Contact geometry
- Gromov non-squeezing theorem
- Symplectic capacity
- Arnold conjecture
- Liouville's theorem (Hamiltonian flow)
- Symplectomorphism
- Marsden-Weinstein symplectic reduction
- Canonical symplectic form on T*M