Tohoku Mathematical Journal

A note on Ribaucour transformations in Lie sphere geometry

Jianquan Ge

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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 $\tau$ which represents the regular Ribaucour sphere congruence $s$ enveloped by the original Legendre submanifold $F$.

Article information

Tohoku Math. J. (2), Volume 67, Number 2 (2015), 273-280.

First available in Project Euclid: 25 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53A40: Other special differential geometries

Ribaucour transformation Lie sphere geometry Legendre submanifold


Ge, Jianquan. A note on Ribaucour transformations in Lie sphere geometry. Tohoku Math. J. (2) 67 (2015), no. 2, 273--280. doi:10.2748/tmj/1435237043.

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