I define equations like the Seiberg-Witten equations for forms of a riemannian manifold $(M,g)$. $\alpha \in \Lambda_+(TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha +\theta \wedge \alpha=0 $$ $$ d\theta_+=\frac{\alpha}{||\alpha||} $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta/f- df/f) $$ Can we define invariants?