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

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 $3$-M\"{o}bius configuration, thus producing explicit solutions depending on arbitrarily many constants.Comment: arXiv admin note: substantial text overlap with arXiv:0808.2007, arXiv:2208.11419; text overlap with arXiv:0905.0216, arXiv:0902.142