Bianchi's B\"{a}cklund transformation for higher dimensional quadrics
  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. 
Ion I. Dinca