On a class of Ribaucour’s normal congruences

The purpose of this paper is to determine all of Ribaucour’s normal congruences such that the invariants of the Laplace equation, corresponding to the conjugate double system of curves of the images of the developables of the sphere, vanish. We give a new proof of the existence ofI-congruences and make some observations concerning Bianchi’s conjecture relative to the congruences of Thybaut. To the memory of Alessandro Terracini