CR manifolds admitting a CR contraction

Details CR manifolds admitting a CR contraction CR manifolds admitting a CR contraction

2008-07-03

arxiv.org/abs/0807.0482v1

Mathematics

Complex Variables

21 pages, 1 figure

Scientific paper

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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