Supersymmetric geometries of IIA supergravity III
We find that (massive) IIA backgrounds that admit a G₂⋉ℝ⁸ invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain 𝔤₂ instanton condition. This result together with those in  and  complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a G₂⋉ℝ⁸ invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.