Explicit absolute parallelism for 2-nondegenerate real hypersurfaces M⁵ ⊂ ℂ³ of constant Levi rank 1

2013/12/22 by Samuel Pocchiola, Pocchiola, Samuel · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.CV

paper · pdf · doi:10.48550/arxiv.1312.6400

55 pages

openalex publication_date 2013/12/22 · arxiv created 2014/05/05 · arxiv updated 2014/05/06 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

We study the local equivalence problem for five dimensional real hypersurfaces M⁵ of ℂ³ which are 2-nondegenerate and of constant Levi rank 1 under biholomorphisms. We find two invariants, J and W, which are expressed explicitly in terms of the graphing function F of M, the annulation of which give a necessary and sufficient condition for M to be locally biholomorphic to a model hypersurface, the tube over the light cone. If one of the two invariants J or W does not vanish on M, we show that the equivalence problem under biholomophisms reduces to an equivalence problem between \e \-structures, that is we construct an absolute parallelism on M.

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• Lie algebras of infinitesimal automorphisms for the model manifolds of general classes \sf II, \sf III₂ and \sf IV₂

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