Deformations of G2-structures with torsion

TL;DR

This paper studies how G2-structures on 7-manifolds deform when torsion is present, providing explicit formulas for torsion changes and differential equations governing the deformation vector.

Contribution

It derives exact formulas for torsion deformations of G2-structures and analyzes conditions for transitions between different torsion classes.

Findings

Explicit torsion deformation formulas derived

Differential equations for deformation vector v established

Certain torsion class transitions shown to have no solutions

Abstract

We consider non-infinitesimal deformations of G2-structures on 7-dimensional manifolds and derive an exact expression for the torsion of the deformed G2-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 G2-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 G2-structures with particular torsions. For some specific torsion classes we find that these equations have no solutions.