arXiv 0812.11042008-12math.CVmath.DG

Normal forms for almost non-integrable CR structures

Dmitri Zaitsev

备注：: Final version as published in AJM
发表信息：: American Journal of Mathematics, 134 (2012), no. 4, 915-947
DOI：: 10.1353/ajm.2012.0027

英文摘要：

We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-CR embeddings that are in some sense "maximally CR". One of the main differences with the classical integrable case is the presence of the non-integrability tensor at the same order as the Levi form, making impossible a good quadric approximation - a key tool in the Chern-Moser theory. Partial normal forms are obtained for general almost CR structures of any CR codimension, in particular, for almost-complex structures. Applications are given to the equivalence problem and the Lie group structure of the group of all CR-diffeomorphisms.

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