Huybrechts, Daniel

Products of harmonic forms and rational curves

Doc. Math., J. DMV 6, 227-239 (2001)


Summary: In general, the product of harmonic forms is not harmonic. We study the top exterior power of harmonic two-forms on compact Kähler manifolds. The non-harmonicity in this case is related to the geometry of the manifold and to the existence of rational curves in particular. K3 surfaces and hyperkähler manifolds are discussed in detail.

Mathematics Subject Classification

14E05, 14J32, 32Q25


harmonic forms, compact Kähler manifolds, Ricci-flat Kähler forms, rational curves