Flat (2,3,5)-Distributions and Chazy's Equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00088799" target="_blank" >RIV/00216224:14310/16:00088799 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3842/SIGMA.2016.029" target="_blank" >http://dx.doi.org/10.3842/SIGMA.2016.029</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3842/SIGMA.2016.029" target="_blank" >10.3842/SIGMA.2016.029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Flat (2,3,5)-Distributions and Chazy's Equations

Popis výsledku v původním jazyce

In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or (2,3,5)-distributions determined by a single function of the form F(q), the vanishing condition for the curvature invariant is given by a 6th order nonlinear ODE. Furthermore, An and Nurowski showed that this ODE is the Legendre transform of the 7th order nonlinear ODE described in Dunajski and Sokolov. We show that the 6th order ODE can be reduced to a 3rd order nonlinear ODE that is a generalised Chazy equation. The 7th order ODE can similarly be reduced to another generalised Chazy equation, which has its Chazy parameter given by the reciprocal of the former. As a consequence of solving the related generalised Chazy equations, we obtain additional examples of flat (2,3,5)-distributions not of the form F(q)=qm.

Název v anglickém jazyce

Flat (2,3,5)-Distributions and Chazy's Equations

Popis výsledku anglicky

In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or (2,3,5)-distributions determined by a single function of the form F(q), the vanishing condition for the curvature invariant is given by a 6th order nonlinear ODE. Furthermore, An and Nurowski showed that this ODE is the Legendre transform of the 7th order nonlinear ODE described in Dunajski and Sokolov. We show that the 6th order ODE can be reduced to a 3rd order nonlinear ODE that is a generalised Chazy equation. The 7th order ODE can similarly be reduced to another generalised Chazy equation, which has its Chazy parameter given by the reciprocal of the former. As a consequence of solving the related generalised Chazy equations, we obtain additional examples of flat (2,3,5)-distributions not of the form F(q)=qm.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

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Svazek periodika

12

Číslo periodika v rámci svazku

29

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

28

Strana od-do

"nestrankovano"

Kód UT WoS článku

000374454900001

EID výsledku v databázi Scopus

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