Convergent normal form for real hypersurfaces at generic Levi degeneracy

Ilya Kossovskiy; Dmitri Zaitsev

Convergent normal form for real hypersurfaces at generic Levi degeneracy

Complex Variables 2014-05-09 v1 Differential Geometry

Authors: Ilya Kossovskiy , Dmitri Zaitsev

Abstract

We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the Levi degeneracy set, that we call \it degenerate chains.

Keywords

real hypersurfaces Levi degeneracy convergent normal form degenerate chains Chern-Moser theory CR geometry

Cite

@article{arxiv.1405.1743,
  title  = {Convergent normal form for real hypersurfaces at generic Levi degeneracy},
  author = {Ilya Kossovskiy and Dmitri Zaitsev},
  journal= {arXiv preprint arXiv:1405.1743},
  year   = {2014}
}

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