Six-Dimensional Nearly Kaehler Manifolds of Cohomogeneity One (II)

Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G= SU_2 X SU_2, and M_reg \subset M its subset of regular points. We show that M_reg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly Kaehler structures and that a 1-parameter subfamily of such structures smoothly extend over a singular orbit of type S^3. This determines a new class of examples of nearly Kaehler structures on TS^3. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM.