Bianchi's B\"{a}cklund transformation for higher dimensional quadrics

TL;DR

This paper generalizes Bianchi's Bäcklund transformation from 2D quadrics to higher dimensions, extending classical deformation theories and transformation techniques to more complex geometric objects.

Contribution

It introduces a higher-dimensional version of Bianchi's theorems and transformation methods for quadrics, broadening the scope of classical differential geometry.

Findings

Extended Bäcklund transformation to higher-dimensional quadrics

Generalized Bianchi's theorems on deformation of quadrics

Provided a framework for transformations in higher dimensions

Abstract

We provide a generalization of Bianchi's B\"{a}cklund 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 B\"{a}cklund transformation for diagonal paraboloids via conjugate systems.