Journal of the
Korean Mathematical Society JKMS

Given an almost complex structure ($\mathbb C^m,J$), $m\ge 2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a^{\alpha}_{\beta}d{\bar z}^{\beta}$, $ \alpha=1,\ldots,m$, to be $(1,0)$-forms, we find conditions on $(a^{\alpha}_{\beta})$ for the existence of holomorphic functions and 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 $S^6$.

Keywords: almost complex manifolds, $J$-holomorphic functions, Nijenhuis tensor, Newlander-Nirenberg theorem

MSC numbers: 32Q60, 32E99, 35J99