We describe the second order obstruction to deformation for nearly $G_2$ structures on compact manifolds. Building on work of Alexandrov and Semmelmann, this allows proving rigidity under deformation for the proper nearly $G_2$ structure on the Aloff–Wallach space $N(1,1)$.

中文翻译：

---

近 G2 结构的变形

我们描述了变形的二阶障碍近 $G_2$紧凑流形上的结构。建立在 Alexandrov 和 Semmelmann 的工作基础上，这可以证明变形下的刚度几乎$G_2$ Aloff-Wallach 空间的结构 $N(1,1)$.