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Pseudoholomorphic Curves in Nearly Kahler $\mathbf{CP}^3$

Feng Xu
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Abstract

We study pseudoholomorphic curves in the nearly Kalher $\mathbf{CP}^3$. It is shown that a class of curves called null-torsion are in one to one correspondence with the integrals of a holomorphic contact system on the usual Kahler $\mathbb{CP}^3$ studied by Bryant. Browing Bryant's result we get plenty of such curves. Rational curves are shown to be either vertical or horizontal or null-torsion. Both horizontal and null-torsion curves can be understood by mentioned Bryant's results while vertical curves are just fibers of the twistor fibration.

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Feng Xu. 2006-05-29. Pseudoholomorphic Curves in Nearly Kahler $\mathbf{CP}^3$. https://arxiv.org/abs/math/0605736

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