I have to show that the direct product of the multi-center Taub-NUT metric with $\mathbb{R}^{3}$ corresponds to a 7-manifold with G2 holonomy.
The metric of the Taub-NUT is:
$ds_{TN}^{2}=V(r)(dr^{2}+r^{2}d\Omega _{2}^{2})+\frac{1}{V(r)}\left ( dy+R\mbox{sin}^{2}\left ( \theta /2 \right )d\phi\right )^{2}$
with $d\Omega _{2}^{2}=d\theta ^{2}+\mbox{sin}^{2}\theta d\phi^{2}$ and $V(r)=1+\frac{R}{2r}$
I don´t know if it will be enough to show that it is Ricci-flat ($R_{mn}=0)$ or trying to find the associative calibration $\Phi$ and show that $\nabla^{g}\Phi=0$ but in this case I don't know how to obtain the components of the three-form $\Phi_{abc}$...
Is there a better way to do so? (I don´t know even if my option would be correct...)