Asian Journal of Mathematics
Volume 20 (2016)
Deformations of $G_2$-structures with torsion
Pages: 123 – 156
We consider non-infinitesimal deformations of $G_2$-structures on 7-dimensional manifolds and derive an exact expression for the torsion of the deformed $G_2$-structure. We then specialize to a case when the deformation is defined by a vector $v$ and we explicitly derive the expressions for the different torsion components of the new $G_2$-structure in terms of the old torsion components and derivatives of $v$. In particular this gives a set of differential equations for the vector $v$ which have to be satisfied for a transition between $G_2$-structures with particular torsions. For some specific torsion classes we find that these equations have no solutions.
$G_2$-structures, deformations, holonomy
2010 Mathematics Subject Classification
53C10, 53C25, 53C29