Darboux’s theorem (symplectic geometry)
If is a -dimensional symplectic manifold, and , then there exists a neighborhood of with a coordinate chart
such that
These are called canonical or Darboux coordinates. On , is the pullback by of the standard symplectic form on , so is a symplectomorphism. Darboux’s theorem implies that there are no local invariants in symplectic geometry, unlike in Riemannian geometry, where there is curvature.
Title | Darboux’s theorem (symplectic geometry) |
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Canonical name | DarbouxsTheoremsymplecticGeometry |
Date of creation | 2013-03-22 13:15:31 |
Last modified on | 2013-03-22 13:15:31 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 6 |
Author | bwebste (988) |
Entry type | Theorem |
Classification | msc 53D05 |
Synonym | Darboux coordinates |