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

RANDALL, Matthew James. Flat (2,3,5)-Distributions and Chazy's Equations. Symmetry, Integrability and Geometry: Methods and Applications. Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, roč. 12, č. 29, s. "nestrankovano", 28 s. ISSN 1815-0659. doi:10.3842/SIGMA.2016.029. 2016.

Základní údaje

• Originální název: Flat (2,3,5)-Distributions and Chazy's Equations
• Autoři: RANDALL, Matthew James (554 Nový Zéland, garant, domácí).
• Vydání: Symmetry, Integrability and Geometry: Methods and Applications, Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, 2016, 1815-0659.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Obor: 10101 Pure mathematics
• Stát vydavatele: Ukrajina
• Utajení: není předmětem státního či obchodního tajemství
• WWW: URL
• Impakt faktor: Impact factor: 0.765
• Kód RIV: RIV/00216224:14310/16:00088799
• Organizační jednotka: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.3842/SIGMA.2016.029
• UT WoS: 000374454900001
• Klíčová slova anglicky: generic rank two distribution in dimension five; conformal geometry; Chazy's equations.
• Štítky: AKR, rivok
• Příznaky: Mezinárodní význam, Recenzováno

Anotace

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. We also give 4-dimensional split signature metrics where their twistor distributions via the An-Nurowski construction have split G2 as their group of symmetries.

Návaznosti

• GBP201/12/G028, projekt VaV: Název: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Grantová agentura ČR, Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku