The multi-moment maps of the nearly Kähler $$S^3\times S^3$$ S 3 × S 3

Abstract

The homogeneous nearly Kähler structure on S 3 × S 3 is the only known complete 6dimensional strictly nearly Kähler structure which is invariant under the action of a 3-torus. We investigate the multi-moment maps associated to such an action and compare with the usual moment map of a toric manifold.