Flat almost complex surfaces in the nearly Kähler S3 × S3
Résumé
In this talk we show how to study almost complex submanifolds of S3 × S3. Compact 6-dimensional non-K¨ahler nearly K¨ahler manifolds do not admit 4-dimensional almost complex submanifolds, so the almost complex submanifolds are surfaces. Previously, a classification of the totally geodesic almost complex surfaces has been obtained as well as the result that an almost complex immersion of a topological 2 sphere is necessary totally geodesic. In this lecture we will show how to obtain a classification, as well as explicit expressions of all almost complex flat surfaces.