Pseudo-holomorphic curves in nearly Kahler CP3

We study pseudo-holomorphic curves in the nearly Kahler 6-manifold CP3. First, we introduce two classes of pseudo-holomorphic curves, called horizontal and null-torsion, respectively. We show that both classes are in one to one correspondence with contact holomorphic curves studied by Bryant in the Kahler manifold CP3. The correspondence between horizontal curves and contact curves can be seen from their definitions. The correspondence between null-torsion and contact curves needs a double fibration to describe. Borrowing Bryant's results, we show that both classes allow Weierstrass representations. Second, we completely characterize pseudo-holomorphic 2-spheres. It is shown that if they are neither vertical nor horizontal, they must have null torsion. (C) 2009 Elsevier B.V. All rights reserved.