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

J 2024

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

KOLÁŘ, Martin; Ilya KOSSOVSKIY a David Gamble SYKES

Základní údaje

Originální název

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

Autoři

KOLÁŘ, Martin; Ilya KOSSOVSKIY a David Gamble SYKES

Vydání

Journal of the London Mathematical Society, Wiley, 2024, 0024-6107

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.200

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/24:00139728

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

CR structures; CR operators and generalizations; Real submanifolds in complex manifolds; Differential geometry of homogeneous manifolds

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 31. 1. 2025 15:02, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GC22-15012J, projekt VaV

Název: Hladká a analytická regularita v CR geometrii (Akronym: SARCG)

Investor: Grantová agentura ČR, Smooth and analytic regularity in CR geometry, Sao Paolo/FAPESP

Citovat

KOLÁŘ, Martin; Ilya KOSSOVSKIY a David Gamble SYKES. New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols. Journal of the London Mathematical Society. Wiley, 2024, roč. 110, č. 2, s. 1-36. ISSN 0024-6107. Dostupné z: https://doi.org/10.1112/jlms.12962.

@article{2472985,
   author = {Kolář, Martin and Kossovskiy, Ilya and Sykes, David Gamble},
   article_number = {2},
   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},
   language = {eng},
   issn = {0024-6107},
   journal = {Journal of the London Mathematical Society},
   title = {New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols},
   url = {https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12962},
   volume = {110},
   year = {2024}
}

TY  - JOUR
ID  - 2472985
AU  - Kolář, Martin - Kossovskiy, Ilya - Sykes, David Gamble
PY  - 2024
TI  - New examples of 2-nondegenerate real hypersurfaces in C^N with arbitrary nilpotent symbols
JF  - Journal of the London Mathematical Society
VL  - 110
IS  - 2
SP  - 1-36
EP  - 1-36
PB  - Wiley
SN  - 00246107
KW  - CR structures
KW  - CR operators and generalizations
KW  - Real submanifolds in complex manifolds
KW  - Differential geometry of homogeneous manifolds
UR  - https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12962
N2  - 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.
ER  -

KOLÁŘ, Martin; Ilya KOSSOVSKIY a David Gamble SYKES. New examples of 2-nondegenerate real hypersurfaces in C\^{}N with arbitrary nilpotent symbols. \textit{Journal of the London Mathematical Society}. Wiley, 2024, roč.~110, č.~2, s.~1-36. ISSN~0024-6107. Dostupné z: https://doi.org/10.1112/jlms.12962.

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