Parabolic conformally symplectic structures II: parabolic contactification

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387249" target="_blank" >RIV/00216208:11320/18:10387249 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10231-017-0719-3" target="_blank" >https://doi.org/10.1007/s10231-017-0719-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-017-0719-3" target="_blank" >10.1007/s10231-017-0719-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parabolic conformally symplectic structures II: parabolic contactification

Popis výsledku v původním jazyce

Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying structure is conformally symplectic, then one obtains a PCS-structure. In the current article, we relate PCS-structures to parabolic contact structures. Starting from a parabolic contact structure with a transversal infinitesimal automorphism, we first construct a natural PCS-structure on any local leaf space of the corresponding foliation. Then we develop a parabolic version of contactification to show that any PCS-structure can be locally realized (uniquely up to isomorphism) in this way. In the second part of the paper, these results are extended to an analogous correspondence between contact projective structures and so-called conformally Fedosov structures. The developments in this article provide the technical background for a construction of sequences and complexes of differential operators which are naturally associated to PCS-structures by pushing down BGG sequences on parabolic contact structures. This is the topic of the third part of this series of articles.

Název v anglickém jazyce

Parabolic conformally symplectic structures II: parabolic contactification

Popis výsledku anglicky

Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying structure is conformally symplectic, then one obtains a PCS-structure. In the current article, we relate PCS-structures to parabolic contact structures. Starting from a parabolic contact structure with a transversal infinitesimal automorphism, we first construct a natural PCS-structure on any local leaf space of the corresponding foliation. Then we develop a parabolic version of contactification to show that any PCS-structure can be locally realized (uniquely up to isomorphism) in this way. In the second part of the paper, these results are extended to an analogous correspondence between contact projective structures and so-called conformally Fedosov structures. The developments in this article provide the technical background for a construction of sequences and complexes of differential operators which are naturally associated to PCS-structures by pushing down BGG sequences on parabolic contact structures. This is the topic of the third part of this series of articles.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-01171S" target="_blank" >GA17-01171S: Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

—

Svazek periodika

197

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

25

Strana od-do

1175-1199

Kód UT WoS článku

000439330700008

EID výsledku v databázi Scopus

2-s2.0-85037609024