The Ribaucour Transformation for Hypersurfaces of Two Space Forms and Conformally Flat Hypersurfaces

摘要

We develop a Ribaucour transformation for the class of conformally flat hypersurfaces f : M-3 - Q(s)(4)(c) with three distinct principal curvatures of a pseudo-Riemannian space form of dimension 4, constant curvature c and index s is an element of{0, 1}, as well as for the class of hypersurfaces f : M-3 - Q(s)(4)(c) with three distinct principal curvatures for which there exists another isometric immersion (f) over tilde : M-3 - Q((s) over tilde)(4)((c) over tilde) with (c) over tilde not equal c. It gives a process to produce a family of new elements of those classes starting from a given one and a solution of a linear system of PDE's. This enables us to construct explicit new examples of hypersurfaces in both classes.