Vertical symmetries of Cartan geometries

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F17%3AA210287S" target="_blank" >RIV/61988987:17310/17:A210287S - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0926224517300499?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0926224517300499?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2017.03.022" target="_blank" >10.1016/j.difgeo.2017.03.022</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Vertical symmetries of Cartan geometries

Popis výsledku v původním jazyce

Elie Cartan's 'espaces generalizes' are, intuitively, curved geometries where the geometrical structure is that of a flat Klein geometry (a homogeneous space of a group) being rolled around a curved manifold without slipping or twisting. In modern terminology we may think of such a Cartan geometry as a fibre bundle with a means of lifting curves in the base manifold to curves in the Lie groupoid of structure-preserving fibre maps. The infinitesimal geometry will then be the Lie algebroid of certain projectable vector field on the fibre bundle, together with a horizontal lift to represent the connection. This paper considers symmetries of these structures, and explains why any vertical symmetry (projecting to the identity on the base manifold of the bundle) or any vertical infinitesimal symmetry (projecting to zero) must necessarily be trivial.

Název v anglickém jazyce

Vertical symmetries of Cartan geometries

Popis výsledku anglicky

Elie Cartan's 'espaces generalizes' are, intuitively, curved geometries where the geometrical structure is that of a flat Klein geometry (a homogeneous space of a group) being rolled around a curved manifold without slipping or twisting. In modern terminology we may think of such a Cartan geometry as a fibre bundle with a means of lifting curves in the base manifold to curves in the Lie groupoid of structure-preserving fibre maps. The infinitesimal geometry will then be the Lie algebroid of certain projectable vector field on the fibre bundle, together with a horizontal lift to represent the connection. This paper considers symmetries of these structures, and explains why any vertical symmetry (projecting to the identity on the base manifold of the bundle) or any vertical infinitesimal symmetry (projecting to zero) must necessarily be trivial.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-02476S" target="_blank" >GA14-02476S: Variace, geometrie a fyzika</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

ISSN

0926-2245

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

165-174

Kód UT WoS článku

000412256400016

EID výsledku v databázi Scopus

2-s2.0-85017103481