Editing Darboux's theorem (section)

=== Comparison with Riemannian geometry ===
Darboux's theorem for symplectic manifolds implies that there are no local invariants in symplectic geometry: a [[Darboux frame|Darboux basis]] can always be taken, valid near any given point. This is in marked contrast to the situation in [[Riemannian geometry]] where the [[curvature of Riemannian manifolds|curvature]] is a local invariant, an obstruction to the [[metric tensor|metric]] being locally a sum of squares of coordinate differentials.

The difference is that Darboux's theorem states that <math> \omega </math> can be made to take the standard form in an ''entire neighborhood'' around ''<math>p </math>''. In Riemannian geometry, the metric can always be made to take the standard form ''at'' any given point, but not always in a neighborhood around that point.