The Ribaucour transformation in Lie sphere geometry

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.

v2: Introduction expanded and references added. 20 pages, 4 Postscript figures

References in corpus (2)

• Discrete differential geometry. Consistency as integrability
• Isothermic surfaces: conformal geometry, Clifford algebras and integrable systems

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