Journal of the
Korean Mathematical Society JKMS

It is well-known that an analytic generic CR submanifold $M$ of codimension $m$ in $\mathbb{C}^{n+m}$ is locally transformed by a biholomorphic mapping to a plane $\mathbb{C}^{n}\times\mathbb{R}^{m}\subset\mathbb{C}^{n}\times\mathbb{C}^{m}$ whenever the Levi form $L$ on $M$ vanishes identically. We obtain such a normalizing biholomorphic mapping of $M$ in terms of the defining function of $M.$ Then it is verified without Frobenius theorem that $M$ is locally foliated into complex manifolds of dimension $n$.

Keywords: CR submanifold, Levi form, biholomorphic mapping

MSC numbers: Primary 32H99