PROPERTIES OF THE NEARLY KAHLER S-3 x S-3

We show how the metric, the almost complex structure and the almost product structure of the homogeneous nearly Kahler S-3 x S-3 can be recovered from a submersion pi : S-3 x S-3 x S-3 -> S-3 x S-3. On S-3 x S-3 x S-3 we have the maps obtained either by changing two coordinates, or by cyclic permutations. We show that these maps project to maps from S-3 x S-3 to S-3 x S-3 and we investigate their behavior.