• Title/Summary/Keyword: Kahler forms

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HARMONIC KAHLER FORMS ON HYPERKAHLER MANIFOLDS

  • Park, Kwang-Soon
    • Communications of the Korean Mathematical Society
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    • v.18 no.3
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    • pp.515-519
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    • 2003
  • 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.

A NOTE ON LOCAL CALIBRATIONS OF ALMOST COMPLEX STRUCTURES

  • Kim, Hyeseon
    • Honam Mathematical Journal
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    • v.44 no.3
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    • pp.384-390
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    • 2022
  • In this paper, we study the obstruction on the jets of an almost complex structure J to the existence of a symplectic form ω such that J is compatible with ω. We describe some almost complex structures on ℝ4 and on ℝ6, respectively, that cannot be calibrated by any symplectic forms. In particular, these examples pertain to the model almost complex structure on ℝ4 in [3], and the simple model structure on ℝ6 in [7].