Parabolic conformally symplectic structures I; definition and distinguished connections

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387195" target="_blank" >RIV/00216208:11320/18:10387195 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1515/forum-2017-0018" target="_blank" >https://doi.org/10.1515/forum-2017-0018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/forum-2017-0018" target="_blank" >10.1515/forum-2017-0018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parabolic conformally symplectic structures I; definition and distinguished connections

Popis výsledku v původním jazyce

We introduce a class of first order G-structures, each of which has an underlying almost conformally symplectic structure. There is one such structure for each real simple Lie algebra which is not of type C-n and admits a contact grading. We show that a structure of each of these types on a smooth manifold M determines a canonical compatible linear connection on the tangent bundle TM. This connection is characterized by a normalization condition on its torsion. The algebraic background for this result is proved using Kostant&apos;s theorem on Lie algebra cohomology. For each type, we give an explicit description of both the geometric structure and the normalization condition. In particular, the torsion of the canonical connection naturally splits into two components, one of which is exactly the obstruction to the underlying structure being conformally symplectic. This article is the first in a series aiming at a construction of differential complexes naturally associated to these geometric structures.

Název v anglickém jazyce

Parabolic conformally symplectic structures I; definition and distinguished connections

Popis výsledku anglicky

We introduce a class of first order G-structures, each of which has an underlying almost conformally symplectic structure. There is one such structure for each real simple Lie algebra which is not of type C-n and admits a contact grading. We show that a structure of each of these types on a smooth manifold M determines a canonical compatible linear connection on the tangent bundle TM. This connection is characterized by a normalization condition on its torsion. The algebraic background for this result is proved using Kostant&apos;s theorem on Lie algebra cohomology. For each type, we give an explicit description of both the geometric structure and the normalization condition. In particular, the torsion of the canonical connection naturally splits into two components, one of which is exactly the obstruction to the underlying structure being conformally symplectic. This article is the first in a series aiming at a construction of differential complexes naturally associated to these geometric structures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Forum Mathematicum

ISSN

0933-7741

e-ISSN

—

Svazek periodika

30

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

19

Strana od-do

733-751

Kód UT WoS článku

000430908100011

EID výsledku v databázi Scopus

2-s2.0-85037819364