We prove the existence of a one-parameter family of nearly parallel G2structures on the manifold S × R, which are mutually non isomorphic and invariant under the cohomogeneity one action of the group SU(2). This family connects the two locally homogeneous nearly parallel G2-structures which are induced by the homogeneous ones on the sphere S.

中文翻译：

---

具有大对称群的近乎平行结构

我们证明了在流形 S × R 上存在一个几乎平行的 G2 结构的单参数族，它们在群 SU(2) 的同质性作用下互不同构且不变。该族连接了由球体 S 上的同质结构引起的两个局部同质的几乎平行的 G2 结构。