Tohoku Mathematical Journal 2015 June SECOND SERIES VOL. 67, NO. 2

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

Title A NOTE ON RIBAUCOUR TRANSFORMATIONS IN LIE SPHERE GEOMETRY

Author Jianquan Ge

(Received December 20, 2013, revised April 8, 2014)
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 $F$.

Mathematics Subject Classification. Primary 53C40; Secondary 53A40.

Key words and phrases. Ribaucour transformation, Lie sphere geometry, Legendre submanifold.