The Ribaucour transformation in Lie sphere geometry

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

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Differential Geometry, 53C40, 37K35 (Primary) 53A40, 53B25 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/120056

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407244
 http://arxiv.org/abs/math/0407244
 Differential Geom. Appl. 24 (2006) 503-520
 doi:10.1016/j.difgeo.2006.04.007

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arXiv