Nearly parallel $G_2$-structures with large symmetry group

Abstract

We prove the existence of a one-parameter family of nearly parallel $G_2$-structures on the manifold $S^3\times {\mathbb{R}}^4$, which are mutually non isomorphic and invariant under the cohomogeneity one action of the group $SU(2{)}^3$. This family connects the two locally homogeneous nearly parallel $G_2$-structures which are induced by the homogeneous ones on the sphere $S^7$.

References in corpus (2)

• 6-dimensional nearly Kaehler manifolds of cohomogeneity one
• Nearly hypo structures and compact Nearly Kähler 6-manifolds with conical singularities