Deformations of nearly $G_2$-structures

Abstract

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

Improved presentation,added full details on rigidity of Aloff-Wallach space $N(1,1)$. 18 pages