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Mathematics > Differential Geometry

arXiv:math/0407244 (math)
[Submitted on 14 Jul 2004 (v1), last revised 25 Apr 2005 (this version, v2)]

Title:The Ribaucour transformation in Lie sphere geometry

Authors:F.E. Burstall, U. Hertrich-Jeromin
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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.
Comments: v2: Introduction expanded and references added. 20 pages, 4 Postscript figures
Subjects: Differential Geometry (math.DG)
MSC classes: 53C40, 37K35 (Primary) 53A40, 53B25 (Secondary)
Cite as: arXiv:math/0407244 [math.DG]
  (or arXiv:math/0407244v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.math/0407244
Journal reference: Differential Geom. Appl. 24 (2006) 503-520
Related DOI: https://doi.org/10.1016/j.difgeo.2006.04.007

Submission history

From: Francis Burstall [view email]
[v1] Wed, 14 Jul 2004 11:08:17 UTC (43 KB)
[v2] Mon, 25 Apr 2005 13:12:40 UTC (44 KB)
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