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arXiv · 1303.1862

A note on Ribaucour transformations in Lie sphere geometry

Jianquan Ge
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Abstract

Following Burstall and Hertrich-Jeromin we study the Ribaucour transformation of Legendre submanifolds in Lie sphere geometry. We give an explicit parametrization of the resulted Legendre submanifold $\hat{F}$ of a Ribaucour transformation, via a single real function $τ$ which represents the regular Ribaucour sphere congruence $s$ enveloped by the original Legendre submanifold $F$.

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Jianquan Ge. 2013-03-08. A note on Ribaucour transformations in Lie sphere geometry. https://arxiv.org/abs/1303.1862

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