Ribaucour transformations of the Surfaces with constant positive Gaussian curvatures in the 3-dimensional Euclidean space

摘要

We associate the surfaces of constant Gaussian curvature $K=1$ with no umbilics to a subclass of the solutions of $O(4,1)/O(3)imes O(1,1)$-system. From this correspondence, we can construct new $K=1$ surfaces from a known $K=1$ surface by using a kind of dressing actions on the solutions of this system.