Bianchi's Bäcklund transformation for higher dimensional quadrics

Abstract

We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the Bäcklund transformation for diagonal paraboloids via conjugate systems.