We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordinates is derived using a Bianchi permutability theorem. Further, we discuss smoothing of semi-discrete curvature line nets and an interpolation by Ribaucour transformations

Burstall, F.