HOLOMORPHIC FUNCTIONS ON ALMOST COMPLEX MANIFOLDS

Title & Authors
HOLOMORPHIC FUNCTIONS ON ALMOST COMPLEX MANIFOLDS
Han, Chong-Kyu; Kim, Hye-Seon;

Abstract
Given an almost complex structure ($\small{\mathbb^{C}^m}$, J), $\small{m\geq2}$, that is defined by setting $\small{\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}}$, $\small{{\alpha}=1,\ldots}$,m, to be (1, 0)-forms, we find conditions on ($\small{a_{\beta}^{\alpha}}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\small{\nu}$,q). Then we determine types for several examples in $\small{\mathbb{C}^2}$ and $\small{\mathbb{C}^3}$ including the natural almost complex structure on $\small{S^6}$.
Keywords
almost complex manifolds;J-holomorphic functions;Nijenhuis tensor;Newlander-Nirenberg theorem;
Language
English
Cited by
1.
Almost complex manifolds with non-degenerate torsion, International Journal of Geometric Methods in Modern Physics, 2016, 1750033
2.
Partial integrability of almost complex structures and the existence of solutions for quasilinear Cauchy–Riemann equations, Pacific Journal of Mathematics, 2013, 265, 1, 59
3.
Invariant submanifolds for systems of vector fields of constant rank, Science China Mathematics, 2016, 59, 7, 1417
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