Lagrangian submanifolds in the homogeneous nearly Kahler S3 x S3

In this paper, we investigate Lagrangian submanifolds in the homogeneous nearly Kahler S-3 x S-3. We introduce and make use of a triplet of angle functions to describe the geometry of a Lagrangian submanifold in S-3 x S-3. We construct a new example of a flat Lagrangian torus and give a complete classification of all the Lagrangian immersions of spaces of constant sectional curvature. As a corollary of our main result, we obtain that the radius of a round Lagrangian sphere in the homogeneous nearly Kahler S-3 x S-3 can only be 2/root 3 or 4/root 3.