Symmetric (2,3,5) distributions, an interesting ODE of 7th order and Plebanski metric

TL;DR

This paper explores a unique seventh-order differential equation with high symmetry, linking it to the geometry of 2-distributions in five dimensions and the Plebanski metric.

Contribution

It identifies a specific 7th order ODE with 10 contact symmetries and connects it to geometric structures in differential geometry.

Findings

The 7th order ODE is uniquely characterized by its symmetry properties.

It naturally arises in the context of 2-distributions in five-dimensional geometry.

The work relates the ODE to the Plebanski metric in differential geometry.

Abstract

We show that the unique 7th order ODE having 10 contact symmetries appears naturally in the theory of generic 2-distributions in dimension five.