Models of CR Manifolds and Their Symmetry Algebras

Result code in 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>

Alternative codes found

RIV/61988987:17310/24:A2503864

Result on the web

<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>

Result language

angličtina

Original language name

Models of CR Manifolds and Their Symmetry Algebras

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10100 - Mathematics

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)

Publication year

2024

Confidentiality

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

Name of the periodical

Advances in Applied Clifford Algebras

ISSN

0188-7009

e-ISSN

1661-4909

Volume of the periodical

34

Issue of the periodical within the volume

3

Country of publishing house

CH - SWITZERLAND

Number of pages

23

Pages from-to

1-23

UT code for WoS article

001262985300001

EID of the result in the Scopus database

2-s2.0-85197561915