2023/04/02 by Kolář, Martin, Kossovskiy, Ilya, Sykes, David · 1 citation
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2304.00619
We introduce a class of uniformly 2-nondegenerate CR hypersurfaces in ℂN, for N>3, having a rank 1 Levi kernel. The class is first of all remarkable by the fact that for every N>3 it forms an \em explicit infinite-dimensional family of everywhere 2-nondegenerate hypersurfaces. To the best of our knowledge, this is the first such construction. Besides, the class an infinite-dimensional family of non-equivalent structures having a given constant nilpotent CR symbol for every such symbol. Using methods that are able to handle all cases with N>5 simultaneously, we solve the equivalence problem for the considered structures whose symbol is represented by a single Jordan block, classify their algebras of infinitesimal symmetries, and classify the locally homogeneous structures among them. We show that the remaining considered structures, which have symbols represented by a direct sum of Jordan blocks, can be constructed from the single block structures through simple linking and extension processes.