Flat Almost Complex Surfaces in the Homogeneous Nearly Kähler S3×S3

By employing a nice adapted frame we prove a Bonnet-type existence and uniqueness theorem for almost complex surfaces in the homogeneous nearly Kähler manifold S 3 × S 3 . The proof uses a local correspondence between almost complex surfaces in S 3 × S 3 and surfaces in R 3 that satisfy the Wente H -surface equation. Furthermore we give a complete classification of flat almost complex surfaces in the homogeneous nearly Kähler S 3 × S 3 .