  We consider deformations of torsion-free G2 structures, defined by the
G2-invariant 3-form $\phi$ and compute the expansion of the Hodge star of
$\phi$ to fourth order in the deformations of $\phi$. By considering M-theory
compactified on a G2 manifold, the G2 moduli space is naturally complexified,
and we get a Kahler metric on it. Using the expansion of the Hodge star of
$\phi$ we work out the full curvature of this metric and relate it to the
Yukawa coupling.
