On the 7th order ODE with submaximal symmetry

Abstract

We find a general solution to the unique 7th order ODE admitting ten dimensional group of contact symmetries. The integral curves of this ODE are rational contact curves in $\PP^3$ which give rise to rational plane curves of degree six. The moduli space of these curves is a real form of the homogeneous space $Sp(4)/SL(2)$.

6 pages, 2 figures. Final version - to appear in JGP

References in corpus (1)

• Paraconformal geometry of $n$th order ODEs, and exotic holonomy in dimension four

Cited by in corpus (4)

• Ordinary differential equations described by their Lie symmetry algebra
• Flat $(2,3,5)$-Distributions and Chazy's Equations
• Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
• On the quadratic invariant of binary sextics