Let (M,ω) be a Kaehler manifold with Ricci curvature Ric. I define 2-forms ρk by the following equations:
ρk(X,Y)=ω(Rick(X),Y)
then we have dρk=0, the 2-forms ρk define Ricci cohomology classes:
˙ρk∈H2(M,R)
How are the Ricci cohomology classes related with the topology of the manifold?