A pair , where is a Manifold and is a Symplectic Form on . The
is a symplectic manifold. Near every point on a symplectic
manifold, it is possible to find a set of local ``Darboux coordinates'' in which the Symplectic Form
has the simple form
See also Manifold, Symplectic Diffeomorphism, Symplectic Form
Sjamaar, R. ``Symplectic Reduction and Riemann-Roch Formulas for Multiplicities.'' Bull. Amer. Math. Soc.
33, 327-338, 1996.