Parabolic conformally symplectic structures I; definition and distinguished connections

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Parabolic conformally symplectic structures I; definition and distinguished connections

Original language description

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.

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

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

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

Name of the periodical

Forum Mathematicum

ISSN

0933-7741

e-ISSN

—

Volume of the periodical

30

Issue of the periodical within the volume

3

Country of publishing house

DE - GERMANY

Number of pages

19

Pages from-to

733-751

UT code for WoS article

000430908100011

EID of the result in the Scopus database

2-s2.0-85037819364