MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Let $\mathcal{M}$ be a symplectic manifold in $\mathbb{R}^4$ of codimension 2 with the symplectic 2-form $dx_1 \wedge dy_1 + dx_2 \wedge dy_2$. Suppose that $\mathcal{M}$ intersects the $(x_2,y_2)$-plane perpendicular in the origin. Does there exist a symplectic transformation $(x_2,y_2) \mapsto (\hat{x}_2,\hat{y}_2)$ such that for an open neighbourhood of the origin in $\mathcal{M}$ the $\hat{x}_2,\hat{y}_2$ are constant zero?