A note on Ribaucour transformations in Lie sphere geometry
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 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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