Products of harmonic forms and rational curves
  In general, the product of harmonic forms is not harmonic. We study the top exterior power of harmonic two-forms on compact Kaehler manifolds. Often, it is not harmonic. This phenomenon is related to the geometry of the manifold and to the existence of rational curves in particular. K3 surfaces and hyperkaehler manifolds are discussed in detail. 
D. Huybrechts