Pseudoholomorphic Curves in Nearly Kahler CP³

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We study pseudoholomorphic curves in the nearly Kalher CP³. 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 CP³ 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.