Models of 2-nondegenerate CR hypersurfaces in C^N

J 2025

Models of 2-nondegenerate CR hypersurfaces in C^N

GREGOROVIČ, Jan; Martin KOLÁŘ a David Gamble SYKES

Základní údaje

Originální název

Models of 2-nondegenerate CR hypersurfaces in C^N

Autoři

GREGOROVIČ, Jan; Martin KOLÁŘ a David Gamble SYKES

Vydání

Mathematische Annalen, Germany, Springer Berlin Heidelberg, 2025, 0025-5831

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.400 v roce 2024

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/25:00144417

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: 29. 8. 2025 13:58, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

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

GREGOROVIČ, Jan; Martin KOLÁŘ a David Gamble SYKES. Models of 2-nondegenerate CR hypersurfaces in C^N. Mathematische Annalen. Germany: Springer Berlin Heidelberg, 2025, roč. 392, č. 2, s. 1615-1663. ISSN 0025-5831. Dostupné z: https://doi.org/10.1007/s00208-025-03138-1.

@article{2514300,
   author = {Gregorovič, Jan and Kolář, Martin and Sykes, David Gamble},
   article_location = {Germany},
   article_number = {2},
   doi = {https://doi.org/10.1007/s00208-025-03138-1},
   keywords = {CR structures; CR operators and generalizations; Real submanifolds in complex manifolds; Differential geometry of homogeneous manifolds},
   language = {eng},
   issn = {0025-5831},
   journal = {Mathematische Annalen},
   title = {Models of 2-nondegenerate CR hypersurfaces in C^N},
   url = {https://link.springer.com/article/10.1007/s00208-025-03138-1},
   volume = {392},
   year = {2025}
}

TY  - JOUR
ID  - 2514300
AU  - Gregorovič, Jan - Kolář, Martin - Sykes, David Gamble
PY  - 2025
TI  - Models of 2-nondegenerate CR hypersurfaces in C^N
JF  - Mathematische Annalen
VL  - 392
IS  - 2
SP  - 1615-1663
EP  - 1615-1663
PB  - Springer Berlin Heidelberg
SN  - 00255831
KW  - CR structures
KW  - CR operators and generalizations
KW  - Real submanifolds in complex manifolds
KW  - Differential geometry of homogeneous manifolds
UR  - https://link.springer.com/article/10.1007/s00208-025-03138-1
N2  - 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.
ER  -

GREGOROVIČ, Jan; Martin KOLÁŘ a David Gamble SYKES. Models of 2-nondegenerate CR hypersurfaces in C\^{}N. \textit{Mathematische Annalen}. Germany: Springer Berlin Heidelberg, 2025, roč.~392, č.~2, s.~1615-1663. ISSN~0025-5831. Dostupné z: https://doi.org/10.1007/s00208-025-03138-1.

Přehled o publikaci