Nearly Parallel G2-structures with Large Symmetry Group

Abstract

AbstractWe prove the existence of a one-parameter family of nearly parallel G2-structures on the manifold $\text{S}^{3}\times \mathbb{R}^{4}$, 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 G2-structures that are induced by the homogeneous ones on the sphere S7.