New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139728" target="_blank" >RIV/00216224:14310/24:00139728 - isvavai.cz</a>

Výsledek na webu

<a href="https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12962" target="_blank" >https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12962</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.12962" target="_blank" >10.1112/jlms.12962</a>

Jazyk výsledku

angličtina

Název v původním jazyce

New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols

Popis výsledku v původním jazyce

We introduce a class of uniformly 2-nondegenerate CR hypersurfaces in C-N, for N &gt; 3, having a rank 1 Levi kernel. The class is first of all remarkable by the fact that for every N &gt; 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 &gt; 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.

Název v anglickém jazyce

New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols

Popis výsledku anglicky

We introduce a class of uniformly 2-nondegenerate CR hypersurfaces in C-N, for N &gt; 3, having a rank 1 Levi kernel. The class is first of all remarkable by the fact that for every N &gt; 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 &gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GC22-15012J" target="_blank" >GC22-15012J: Hladká a analytická regularita v CR geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the London Mathematical Society

ISSN

0024-6107

e-ISSN

1469-7750

Svazek periodika

110

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

1-36

Kód UT WoS článku

001288981200004

EID výsledku v databázi Scopus

2-s2.0-85199141265