The Ribaucour transformation in Lie sphere geometry

Details The Ribaucour transformation in Lie sphere geometry The Ribaucour transformation in Lie sphere geometry

2004-07-14

arxiv.org/abs/math/0407244v2

Differential Geom. Appl. 24 (2006) 503-520

Mathematics

Differential Geometry

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

Scientific paper

10.1016/j.difgeo.2006.04.007

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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