New examples of 2-nondegenerate real hypersurfaces in CN with arbitrary nilpotent symbols

We introduce a class of uniformly 2-nondegenerate CR hypersurfaces in C-N, 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 explicit infinite-dimensional family of every where 2-nondegenerate hypersurfaces. To the best of our knowledge, this is the first such construction. Besides, the class contains infinite-dimensional families of nonequivalent structures having a given constant nilpotent CR symbol for every such symbol. Using methods that are able to handle all cases with N > 5simultaneously, 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.