Convergent normal form for real hypersurfaces at generic Levi degeneracy

2014/05/07 by Ilya Kossovskiy, Kossovskiy, Ilya, Dmitri Zaitsev +1
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1405.1743

arxiv created 2014/05/07 · arxiv updated 2014/05/09

Abstract

We construct a complete convergent normal form for a real hypersurface in \CCN, N≥ 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 \citechern, distinguished curves in the Levi degeneracy set, that we call \it degenerate chains.

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