  We consider backgrounds of (massive) IIA supergravity of the form of a warped
product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact
manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We
analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on
manifolds of SU(2) structure. We prove the absence of solutions in certain
cases.
