Models of 2-nondegenerate CR hypersurfaces in C^N

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144417" target="_blank" >RIV/00216224:14310/25:00144417 - isvavai.cz</a>
Alternative codes found
RIV/61988987:17310/25:A2603AWL
Result on the web
<a href="https://link.springer.com/article/10.1007/s00208-025-03138-1" target="_blank" >https://link.springer.com/article/10.1007/s00208-025-03138-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00208-025-03138-1" target="_blank" >10.1007/s00208-025-03138-1</a>

Result language
angličtina
Original language name
Models of 2-nondegenerate CR hypersurfaces in C^N
Original language description
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 which we introduce are essential CR invariants playing the same fundamental role as quadrics do in the classical Levi nondegenerate case. In particular, we show that each real analytic uniformly 2-nondegenerate hypersurface in {mathbb {C}}^N is a perturbation of a 2-nondegenerate model. We give a complete characterization of all 2-nondegenerate models and show that the moduli space of such hypersurfaces in {mathbb {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 (modified symbols), and show how to compute these intrinsically defined invariants from a model's defining equation. Moreover, we show that these models automatically possess infinitesimal symmetries spanning a complement to their Levi kernel and derive explicit formulas for such symmetries.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GC22-15012J" target="_blank" >GC22-15012J: Smooth and analytic regularity in CR geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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