Deformations of G2-structures with torsion

Printer-friendly version
Sergey Grigorian
Stony Brook
Tue, 04/10/2012 - 4:00pm
RH 306

We consider non-infinitesimal deformations of G2-structures on 7-dimensional
manifolds and derive a closed expression for the torsion of the deformed
G2-structure. We then specialize to the case where the deformation lies in
the seven-dimensional representation of G2 and is hence defined by a vector
v. In this case, 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 then explore the solutions of these equations.