Towards reduction of type II theories on SU(3) structure manifolds

We revisit the reduction of type II supergravity on SU( 3) structure manifolds conjectured to lead to gauged N = 2 supergravity in 4 dimensions. The reduction proceeds by expanding the invariant 2- and 3-forms of the SU( 3) structure as well as the gauge potentials of the type II theory in the same set of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions. By focussing on the metric sector, we arrive at a list of constraints these expansion forms should satisfy to yield a base point independent reduction. Identifying these constraints is a first step towards a first-principles reduction of type II on SU( 3) structure manifolds.