Is there any classification result(s) regarding how many symplectic structures on CP^n?



How many Symplectic Structures on CP^n?
One of the headline consequences of Taubes' work on Seiberg-Witten theory on symplectic four- manifolds was that the standard symplectic form on $\mathbb{C}P^2$ is the unique one (up to scale, of course); see Theorem B of [this paper](http://www.mrlonline.org/mrl/1995-002-002/1995-002-002-010.html). Of course for $\mathbb{C}P^1$ the same result holds---just use the Moser trick. 


I'm not aware of any progress on this problem for $n>2$.


