Harmonic K\＂{a}hler forms on hyperk\＂{a}hler manifolds
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Let M be a hyperkahler manifold with the hyperkahler structure (g, I, J, K). In [5], D. Huybrechts suggests that it is an open and interesting question whether any Kahler class that stays Kahler in the twister family can actually be represented by an harmonic Kahler form. In this paper we will consider both this problem and the set of all the primitive harmonic Kahler forms on M.
Abstract
Let M be a hyperk"{a}hler manifold with the hyperk"{a}hler structure (g,I,J,K). In [5], D. Huybrechts suggeststhat it is an open and interesting question whether any K"{a}hler class that stays K"{a}hler in the twistor familycan actually be represented by an harmonic K"{a}hler form. In this paper we will consider both this problem and theset of all the primitive harmonic K"{a}hler forms on M.