Generalized stationary discs attached to degenerate submanifolds in ${\mathbb{C}}^N$

We study the family of generalized stationary discs attached to a Levi degenerate submanifold M of codimension d in ${\mathbb{C}}^{n+d}$. We show, under suitable geometric assumptions on M, that this family forms a finite dimensional real submanifold of the Banach space of analytic discs.