Tohoku Mathematical Journal

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

Article information

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

Dates
First available in Project Euclid: 25 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1435237043

Digital Object Identifier
doi:10.2748/tmj/1435237043

Mathematical Reviews number (MathSciNet)
MR3365372

Zentralblatt MATH identifier
1328.53016

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

Keywords
Ribaucour transformation Lie sphere geometry Legendre submanifold

Citation

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. https://projecteuclid.org/euclid.tmj/1435237043


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References

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