A normal form for a real 2-codimensional submanifold in ${\mathbb{C}}^{N+1}$ near a CR singularity

We construct a formal normal form for a real 2-codimensional submanifold $M\subset {\mathbb{C}}^{N+1}$ near a CR singularity approximating the sphere. This result gives a higher dimensional extension of Huang-Yin’s normal form in ${\mathbb{C}}^2$.