Six-dimensional spaces defined by the equations of KN and KdV

TL;DR

This paper constructs six-dimensional metrics derived from solutions of the Krichever-Novikov and KdV equations, exploring their properties based on three-dimensional flat metrics obtained via KdV solutions.

Contribution

It introduces new six-dimensional metrics defined by solutions of KN and KdV equations, expanding geometric structures linked to integrable systems.

Findings

Six-dimensional metrics constructed from KdV solutions

Properties of these metrics analyzed

Examples based on solutions of KN and KdV equations

Abstract

On base of three-dimensional flat metrics obtained with the help of solutions of the KdV-equation were constructed the examples of six-dimensional metrics, which are determined by the help of solutions of Krichever-Novikov and KdV. Their properties are discussed.