Flat (2,3,5)-Distributions and Chazy's Equations
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Flat (2,3,5)-Distributions and Chazy's Equations
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry, Integrability and Geometry: Methods and Applications
ISSN
1815-0659
e-ISSN
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Volume of the periodical
12
Issue of the periodical within the volume
29
Country of publishing house
UA - UKRAINE
Number of pages
28
Pages from-to
"nestrankovano"
UT code for WoS article
000374454900001
EID of the result in the Scopus database
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