Reduced Vectorial Ribaucour Transformation for the Darboux-Egoroff Equations

The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lamé type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transformations. Finally, as an example, we apply these transformations to the Cartesian background. On leave of absence from Beijing Graduate School, CUMT, Beijing 100083, China Supported by Beca para estancias temporales de doctores y tecnólogos extranjeros en España: SB95-A01722297 Partially supported by CICYT: proyecto PB95–0401 1