• 제목/요약/키워드: Newlander-Nirenberg theorem

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HOLOMORPHIC FUNCTIONS ON ALMOST COMPLEX MANIFOLDS

  • Han, Chong-Kyu;Kim, Hye-Seon
    • 대한수학회지
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    • 제49권2호
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    • pp.379-394
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    • 2012
  • Given an almost complex structure ($\mathbb^{C}^m$, J), $m\geq2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}$, ${\alpha}=1,\ldots$,m, to be (1, 0)-forms, we find conditions on ($a_{\beta}^{\alpha}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\nu$,q). Then we determine types for several examples in $\mathbb{C}^2$ and $\mathbb{C}^3$ including the natural almost complex structure on $S^6$.