Vectorial Ribaucour transformations for the Lame equations

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The vectorial extension of the Ribaucour transformation for the Lame equations bf orthogonal conjugate nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background.
©IOP Publishing LTD. M. M. would like to thank several conversations with A. Doliwa and P. M. Santini. In particular, A. Doliwa’s historical remarks were quite useful.
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