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On the Moser normal form at a non-umbilic point. (English) Zbl 0358.32013
Any analytic real hypersurface $$M^{2n+1}$$ in $$\mathbb{C}^{n+1}$$, $$n\geq 1$$with non-degenerate Levi form at a point $$p$$ has a normal form relative to certain holomorphic coordinate systems centered at $$p$$ [S. S. Chern and J. K. Moser, Acta math. 133 (1974), 219-271 (1975; Zbl 0302.32015)]. The normal form is determined up to the action of a non-compact isotropy group. For $$M^3\subset \mathbb{C}^2$$ Moser has given further normalizations which reduce this isotropy group to $$\mathbb{Z}_2$$ when $$p$$ is a non-umbilic point. In this paper it is shown how to make analogous further normalization at a non-umbilic point when $$m\geq 2$$. The isotropy group is reduced to $$U(n) \times \mathbb{Z}_2$$. In the generic case it is shown how to reduce the isotropy group to a finite group. The method is to make use of the pseudo-conformal connection and certain normalizations of it carried out by the author in a previous paper.
Reviewer: S. M. Webster

##### MSC:
 32C99 Analytic spaces 32Q99 Complex manifolds
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##### References:
 [1] Chern, S.S., Moser, J.K.: Real hypersurfaces in complex manifolds. Acta Math.133, 219-271 (1974) · Zbl 0302.32015 [2] Webster, S.: Pseudo-hermitian structures on a real hypersurface. Diff. Geom. (to appear) · Zbl 0379.53016
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