Bianchi's B\"acklund transformation for higher dimensional quadrics
Abstract
We provide a generalization of Bianchi's B\"acklund 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\"acklund transformation for diagonal paraboloids via conjugate systems.
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