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

Abstract : 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 S3×S3. The proof uses a local correspondence between almost complex surfaces in S3×S3 and surfaces in R3 that satisfy the Wente H-surface equation. Furthermore we give a complete classification of flat almost complex surfaces in the homogeneous nearly Kähler S3×S3.