CR manifolds admitting a CR contraction

2008/07/03 by Kang‐Tae Kim, Kim, Kang-Tae, Jean-Christophe Yoccoz +1
Mathematics · #32V20 #32V40 #37F99 #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0807.0482

openalex publication_date 2008/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the germs of C^∞ CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into \CCⁿ 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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