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

Abstract

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 $\mathbb{C}^{2}$.