CR manifolds admitting a CR contraction

Kang-Tae Kim; Jean-Christophe Yoccoz

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arXiv · 0807.0482

CR manifolds admitting a CR contraction

Kang-Tae Kim·Jean-Christophe Yoccoz

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Abstract

We classify the germs of $\mathcal{C}^\infty$ CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into $\CC^n$ as a real hypersurface defined by a polynomial defining function consisting of monomials whose degrees are completely determined by the extended resonances of the contraction. Furthermore the contraction map extends to a holomorphic contraction that coincides in fact with its polynomial normal form. Consequently, several results concerning Complex and CR geometry are derived.

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Kang-Tae Kim, Jean-Christophe Yoccoz. 2008-07-03. CR manifolds admitting a CR contraction. https://arxiv.org/abs/0807.0482

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