New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres

摘要: There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on 6-sphere induced by octonionic multiplication. Nearly 6-manifolds play distinguished role both in general and also because their connection with singular spaces holonomy group compact exceptional Lie G2: metric cone over Riemannian 6-manifold M has contained G2 if only 6-manifold. A central problem field been absence any complete inhomogeneous examples. We prove existence first proving at least one cohomogeneity product pair 3-spheres. conjecture that these are simply connected (inhomogeneous) structures six dimensions.