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

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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.