Models of CR Manifolds and Their Symmetry Algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139731" target="_blank" >RIV/00216224:14310/24:00139731 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61988987:17310/24:A2503864

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00006-024-01341-y" target="_blank" >https://link.springer.com/article/10.1007/s00006-024-01341-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00006-024-01341-y" target="_blank" >10.1007/s00006-024-01341-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Models of CR Manifolds and Their Symmetry Algebras

Popis výsledku v původním jazyce

In this paper we give an exposition of several recent results on local symmetries of real submanifolds in complex space, featuring new examples and important corollaries. Departing from Levi non-degenerate hypersurfaces, treated in the classical Chern–Moser theory, we explore three important classes of manifolds, which naturally extend the classical case. We start with quadratic models for real submanifolds of higher codimension and review some recent striking results, which demonstrate that such higher codimension models may possess symmetries of arbitrarily high jet degree. This disproves the long held belief that the fundamental 2-jet determination results from Chern–Moser theory extend to this case. As a second case, we consider hypersurfaces with singular Levi form at a point, which are of finite multitype. This leads to the study of holomorphically nondegenerate polynomial models. We outline several results on their symmetry algebras including a characterization of models admitting nonlinear symmetries. In the third part we consider the class of structures with everywhere singular Levi forms that has received the most attention recently, namely everywhere 2-nondegenerate structures. We present a computation of their Catlin multitype and results on symmetry algebras of their weighted homogeneous (w.r.t. multitype) models.

Název v anglickém jazyce

Models of CR Manifolds and Their Symmetry Algebras

Popis výsledku anglicky

In this paper we give an exposition of several recent results on local symmetries of real submanifolds in complex space, featuring new examples and important corollaries. Departing from Levi non-degenerate hypersurfaces, treated in the classical Chern–Moser theory, we explore three important classes of manifolds, which naturally extend the classical case. We start with quadratic models for real submanifolds of higher codimension and review some recent striking results, which demonstrate that such higher codimension models may possess symmetries of arbitrarily high jet degree. This disproves the long held belief that the fundamental 2-jet determination results from Chern–Moser theory extend to this case. As a second case, we consider hypersurfaces with singular Levi form at a point, which are of finite multitype. This leads to the study of holomorphically nondegenerate polynomial models. We outline several results on their symmetry algebras including a characterization of models admitting nonlinear symmetries. In the third part we consider the class of structures with everywhere singular Levi forms that has received the most attention recently, namely everywhere 2-nondegenerate structures. We present a computation of their Catlin multitype and results on symmetry algebras of their weighted homogeneous (w.r.t. multitype) models.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - 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

Advances in Applied Clifford Algebras

ISSN

0188-7009

e-ISSN

1661-4909

Svazek periodika

34

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

001262985300001

EID výsledku v databázi Scopus

2-s2.0-85197561915