specifically, a symplectic manifold structure is a stronger concept than a "g"-structure for the symplectic group. a symplectic structure on a manifold is a two-form "ω" on "m" that is non-degenerate (which is an formula_38-structure, or almost symplectic structure), "together with" the extra condition that d"ω" = 0; this latter is called an integrability condition.