In this article, we give a normal form for real-analytic, Levi-nondegenerate submanifolds of ${ℂ}^N$ of codimension $d\ge 1$ under the action of formal biholomorphisms. We find a very general sufficient condition on the formal normal form that ensures that the normalizing transformation to this normal form is holomorphic. In the case $d=1$ our methods in particular allow us to obtain a new and direct proof of the convergence of the Chern–Moser normal form.

中文翻译：

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Chern-Moser-Beloshapka范式的收敛性

在本文中，我们给出了实分析的Levi非退化子流形的范式 ${ℂ}^{ñ}$ 维数 $d\ge \mathrm{1个}$在形式全同构的作用下。我们在形式范式上找到了一个非常一般的充分条件，可以确保对此范式的归一化变换是全纯的。在这种情况下$d=\mathrm{1个}$ 特别是我们的方法使我们能够获得有关Chern-Moser法线形式收敛的新的直接证明。