The closed invariant characterization conjecture for irreducible Wintgen ideal submanifolds

Let $M^k$ be an irreducible Wintgen ideal submanifold of dimension $k\ge 3$, meaning that the only integrable distribution containing the canonical distribution $\mathbb{D}_2$ is the tangent bundle of $M$. Let $\omega={\rm d}Y\cdot\hat{Y}$ be the Lorentz-plane connection 1-form associated with a frame $\{Y,\hat{Y},\eta_1,\eta_2,\eta_a\}$. Closed invariant characterization conjecture. If

$${\rm d}\omega=0,$$

then $M^k$ is Möbius equivalent to a minimal Wintgen ideal submanifold in one of the three space forms. The characterization is known for $m=3,p=2$ and for the general 3-dimensional case; it remains open in higher dimensions.