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.

引用

页码：503 / 520

页数：18

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