The Geometry of $\mathcal{N}=3$ AdS$_4$ in Massive IIA

The geometry of the N=3, SO(4)-invariant, AdS4 solution of massive type IIA supergravity that uplifts from the N=3 vacuum of D=4 N=8 dyonic ISO(7) supergravity is investigated. Firstly, a D=4, SO(4)-invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)-invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the N=3 AdS4 solution in massive IIA and analyse its geometry. Locally, the internal S6 geometry corresponds to a warped fibration of S2 and a hemisphere of S4. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the N=3 solution are constructed and shown to obey the massive type IIA Killing spinor equations.