Publication details
New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Journal of the London Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| web | https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12962 |
| Doi | https://doi.org/10.1112/jlms.12962 |
| Keywords | CR structures; CR operators and generalizations; Real submanifolds in complex manifolds; Differential geometry of homogeneous manifolds |
| Description | 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. |
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