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Explicit Absolute Parallelism for 2-Nondegenerate Real Hypersurfaces \(M^5 \subset \mathbb {C}^3\) of Constant Levi Rank 1

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Abstract

We study the local equivalence problem under biholomorphisms for five-dimensional real hypersurfaces \(M^5\) of \(\mathbb {C}^3\) which are 2-nondegenerate and of constant Levi rank 1. We find exactly two invariants, J and W, which are expressed explicitly in terms of the graphing function F of M, the vanishing of which gives 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 biholomorphisms reduces to an equivalence problem between \(\{e \}\)-structures, that is, we construct an absolute parallelism on M.

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  1. Département de Mathématiques, Faculté des sciences d’Orsay, Université Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Joël Merker & Samuel Pocchiola

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  1. Joël Merker
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  2. Samuel Pocchiola
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Correspondence to Joël Merker.

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Merker, J., Pocchiola, S. Explicit Absolute Parallelism for 2-Nondegenerate Real Hypersurfaces \(M^5 \subset \mathbb {C}^3\) of Constant Levi Rank 1. J Geom Anal 30, 2689–2730 (2020). https://doi.org/10.1007/s12220-018-9988-3

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  • DOI: https://doi.org/10.1007/s12220-018-9988-3

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