  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 result. Further,
we discuss smoothing of semi-discrete curvature line nets and an interpolation
by Ribaucour transformations.
