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 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.

2000 Mathematics Subject Classification: 14E05, 14J32, 32Q25

Keywords and Phrases: Harmonic forms, compact Kähler manifolds, Ricci-flat Kähler forms, rational curves

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