The Ribaucour transformation in Lie sphere geometry
Differential Geometry
2007-05-23 v2
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.
Cite
@article{arxiv.math/0407244,
title = {The Ribaucour transformation in Lie sphere geometry},
author = {F. E. Burstall and U. Hertrich-Jeromin},
journal= {arXiv preprint arXiv:math/0407244},
year = {2007}
}
Comments
v2: Introduction expanded and references added. 20 pages, 4 Postscript figures