Editing Symplectic manifold (section)

=== Kähler manifolds ===
A [[Kähler manifold]] is a symplectic manifold equipped with a compatible integrable complex structure. They form a particular class of [[complex manifold]]s. A large class of examples come from complex [[algebraic geometry]]. Any smooth complex [[projective variety]] <math>V \subset \mathbb{CP}^n</math> has a symplectic form which is the restriction of the [[Fubini-Study metric|Fubini—Study form]] on the [[projective space]] <math>\mathbb{CP}^n</math>.