The B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center

TL;DR

This paper explicitly derives Bäcklund transforms for Peterson's isometric deformations of diagonal higher-dimensional quadrics without center, enabling iterative solution generation via classical theorems and configurations.

Contribution

It provides explicit formulas for Bäcklund transforms of Peterson's deformations and demonstrates their iterative application using classical geometric theorems.

Findings

Explicit Bäcklund transforms derived

Transforms can be iterated via Bianchi Permutability

Solutions depend on arbitrarily many constants

Abstract

We provide the B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center. These are found explicitly. can be iterated via the Bianchi Permutability Theorem and can be further iterated via the $3$-moving M\"{o}bius configuration, thus producing explicit solutions depending on arbitrarily many constants.