New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols
Original language 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of the London Mathematical Society
ISSN
0024-6107
e-ISSN
1469-7750
Volume of the periodical
110
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
36
Pages from-to
1-36
UT code for WoS article
001288981200004
EID of the result in the Scopus database
2-s2.0-85199141265