Models of 2-nondegenerate CR hypersurface in ℂ^N

2024/04/09 by Gregorovič, Jan, Kolář, Martin, Sykes, David
#32V05 #32V40 #53C30 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.06525

Abstract

We show that every point in a uniformly 2-nondegenerate CR hypersurface is canonically associated with a model 2-nondegenerate structure. The 2-nondegenerate models are basic CR invariants playing the same fundamental role as quadrics do in the Levi nondegenerate case. We characterize all 2-nondegenerate models and show that the moduli space of such hypersurfaces in ℂ^N is infinite dimensional for each N>3. We derive a normal form for these models' defining equations that is unique up to an action of a finite dimensional Lie group. We generalize recently introduced CR invariants termed modified symbols, and show how to compute these intrinsically defined invariants from a model's defining equation. We show that these models automatically possess infinitesimal symmetries spanning a complement to their Levi kernel and derive explicit formulas for them.

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