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The Ribaucour transformation in Lie sphere geometry

F. E. Burstall·U. Hertrich-Jeromin
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Abstract

We discuss the Ribaucour transformation of Legendre maps in Lie sphere geometry. In this context, we give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer--Tojeiro. We go on to formulate and prove a higher dimensional version of the Permutability Theorem. It is shown how these theorems descend to the corresponding results for submanifolds in space forms.

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F. E. Burstall, U. Hertrich-Jeromin. 2005-04-25. The Ribaucour transformation in Lie sphere geometry. https://doi.org/10.1016/j.difgeo.2006.04.007

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