G2-structure deformations and warped products
  We overview the properties of non-infinitesimal deformations of G2-structures on seven-manifolds, and in particular, focus on deformations that lie in the seven-dimensional representation of G2 and are thus defined by a vector. We then consider deformations from G2-structures with the torsion class having one-dimensional and seven-dimensional components (so-called conformally nearly parallel G2-manifolds) to G2-structures with just a one-dimensional torsion component (nearly parallel G2-manifolds). We find that deformations between such structures exist if and only if the metric is a particular warped product metric. 
Sergey Grigorian
math.DG