Preprint A15/2001
An extension of the classical Ribaucour transformation

Ruy Tojeiro | Dajczer, Marcos

**Keywords: **
Ribaucour transformation

The classical Ribaucour transformation is
extended to submanifolds with arbitrary dimension and codimension of a
pseudo-Riemannian space form. Ribaucour transforms of a submanifold are
shown to be in correspondence with commuting symmetric Codazzi tensors. A
main application is a parameterization, in terms of solutions of a completely
integrable linear first order system of PDE's, of all Ribaucour transforms
of a given submanifold with constant sectional curvature which have the same
constant curvature. In particular, many explicit examples are obtained,
some of them are the first of their kind.
A permutability result is proved which allows to produce further examples by
a simple algebraic procedure once two Ribaucour transforms of a given
submanifold are known.