# Nurowski's conformal class of a maximally symmetric (2,3,5)-distribution and its Ricci-flat representatives

## TL;DR

This paper demonstrates how solutions to specific differential equations related to the generalized Chazy equation naturally appear in the process of conformally rescaling metrics within Nurowski's class, leading to Ricci-flat representatives.

## Contribution

It establishes a connection between solutions of the generalized Chazy equation and Ricci-flat metrics in Nurowski's conformal class for maximally symmetric (2,3,5)-distributions.

## Key findings

- Solutions to the generalized Chazy equation appear in conformal rescaling.
- Conformal rescaling can produce Ricci-flat metrics within the class.
- The work links differential equations to geometric structures in conformal geometry.

## Abstract

We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters $k=2$ and $k=3$ naturally show up in the conformal rescaling that takes a representative metric in Nurowski's conformal class associated to a maximally symmetric $(2,3,5)$-distribution (described locally by a certain function $\varphi(x,q)=\frac{q^2}{H''(x)}$) to a Ricci-flat one.