Bundles of Weyl structures and invariant calculus for parabolic geometries

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134301" target="_blank" >RIV/00216224:14310/23:00134301 - isvavai.cz</a>

Výsledek na webu

<a href="https://bookstore.ams.org/view?ProductCode=CONM/788" target="_blank" >https://bookstore.ams.org/view?ProductCode=CONM/788</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/conm/788/15819" target="_blank" >10.1090/conm/788/15819</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bundles of Weyl structures and invariant calculus for parabolic geometries

Popis výsledku v původním jazyce

For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general tools were presented for the entire class of parabolic geometries, i.e., the Cartan geometries modelled on homogeneous spaces $G/P$ with $P$ a parabolic subgroup in a semi-simple Lie group $G$. Similarly to conformal Riemannian and projective structures, all these geometries determine a class of distinguished affine connections, which carry an affine structure modelled on differential 1-forms $Upsilon$. They correspond to reductions of $P$ to its reductive Levi factor, and they are called the Weyl structures similarly to the conformal case. The standard definition of differential invariants in this setting is as affine invariants of these connections, which do not depend on the choice within the class. In this article, we describe a universal calculus which provides an important first step to determine such invariants. We present a natural procedure how to construct all affine invariants of Weyl connections, which depend only tensorially on the deformations $Upsilon$.

Název v anglickém jazyce

Bundles of Weyl structures and invariant calculus for parabolic geometries

Popis výsledku anglicky

For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general tools were presented for the entire class of parabolic geometries, i.e., the Cartan geometries modelled on homogeneous spaces $G/P$ with $P$ a parabolic subgroup in a semi-simple Lie group $G$. Similarly to conformal Riemannian and projective structures, all these geometries determine a class of distinguished affine connections, which carry an affine structure modelled on differential 1-forms $Upsilon$. They correspond to reductions of $P$ to its reductive Levi factor, and they are called the Weyl structures similarly to the conformal case. The standard definition of differential invariants in this setting is as affine invariants of these connections, which do not depend on the choice within the class. In this article, we describe a universal calculus which provides an important first step to determine such invariants. We present a natural procedure how to construct all affine invariants of Weyl connections, which depend only tensorially on the deformations $Upsilon$.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

The Diverse World of PDEs : Geometry and Mathematical Physics

ISBN

9781470471477

ISSN

0271-4132

e-ISSN

—

Počet stran výsledku

20

Strana od-do

53-72

Název nakladatele

American Mathematical Society

Místo vydání

Rhode Island (USA)

Místo konání akce

Moscow

Datum konání akce

13. 12. 2021

Typ akce podle státní příslušnosti

CST - Celostátní akce

Kód UT WoS článku

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