$G_2$-Holonomy Metrics Connected with a 3-Sasakian Manifold
  We construct complete noncompact Riemannian metrics with $G_2$-holonomy on noncompact orbifolds that are $\Bbb R^3$-bundles with the twistor space $\mathcal{Z}$ as a spherical fiber. 
Yaroslav V. Bazaikin, Eugene G. Malkovich