Résume | A long-standing problem in almost complex geometry has been the question of existence of (complete) inhomogeneous nearly Kähler 6-manifolds. One of the main motivations for this question comes from geometry: the Riemannian cone over a nearly Kähler 6-manifold is a singular space with holonomy G2. Viewing Euclidean 7-space as the cone over the round 6-sphere, the induced nearly Kähler structure is the standard G2-invariant almost complex structure on the 6-sphere induced by octonionic multiplication. We resolve this problem by proving the existence of exotic (inhomogeneous) nearly Kahler metrics on the 6-sphere and also on the product of two 3-spheres. This is joint work with Lorenzo Foscolo, Stony Brook. |