The Ribaucour transformation in Lie sphere geometry

被引：13
|
作者：
Burstall, F. E. [1 ]
Hertrich-Jeromin, U. [1 ]
机构：
[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2006年 / 24卷 / 05期
关键词：
Ribaucour transformation; submanifold; Lie geometry; Bianchi permutability; Legendre map;
D O I：
10.1016/j.difgeo.2006.04.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss the Ribaucour transformation of Legendre (contact) maps in its natural context: Lie sphere geometry. We give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer-Tojeiro as well as a higher dimensional version with the combinatorics of a cube. We also show how these theorems descend to the corresponding results for submanifolds in space forms. (C) 2006 Elsevier B.V. All rights reserved.
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页码：503 / 520
页数：18
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