# HOLOMORPHIC FUNCTIONS ON ALMOST COMPLEX MANIFOLDS

• Han, Chong-Kyu (Department of Mathematical Sciences Seoul National University) ;
• Kim, Hye-Seon (Department of Mathematical Sciences Seoul National University)
• Published : 2012.03.01
• 85 23

#### Abstract

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 $S^6$.

#### Keywords

almost complex manifolds;J-holomorphic functions;Nijenhuis tensor;Newlander-Nirenberg theorem

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#### Cited by

1. Partial integrability of almost complex structures and the existence of solutions for quasilinear Cauchy–Riemann equations vol.265, pp.1, 2013, https://doi.org/10.2140/pjm.2013.265.59
2. Invariant submanifolds for systems of vector fields of constant rank vol.59, pp.7, 2016, https://doi.org/10.1007/s11425-016-5139-0