Maurer - Cartan Forms of the Symmetry Pseudo-Group and the Covering of Plebanski's Second Heavenly Equation

TL;DR

This paper derives Wahlquist-Estabrook forms for the covering of Plebanski's second heavenly equation using Maurer-Cartan forms of its symmetry pseudo-group, advancing the understanding of its geometric structure.

Contribution

It introduces a novel method linking Maurer-Cartan forms to Wahlquist-Estabrook forms for Plebanski's equation, providing new insights into its symmetry structure.

Findings

Derived Wahlquist-Estabrook forms from Maurer-Cartan forms

Connected symmetry pseudo-group to geometric coverings

Enhanced understanding of Plebanski's second heavenly equation

Abstract

We derive Wahlquist - Estabrook forms of the covering of Plebanski's second heavenly equation from Maurer - Cartan forms of its symmetry pseudo-group.