分野別セミナー

We shall discuss a variety of results for the Ribaucour transformation of (smooth and discrete) curves, in particular, we will discuss a result on the reduction of the ambient dimension via Ribaucour transformation that also holds in higher dimensions and yields the classical notion of Ribaucour coordinates for surfaces. Using a Bianchi permutability result,this dimension reduction leads to an interpolation result for the Ribaucour transformation, hence to a method to construct (semi-)discrete principal nets from boundary data.