We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordinates is derived using a Bianchi permutability theorem. Further, we discuss smoothing of semi-discrete curvature line nets and an interpolation by Ribaucour transformations.
CITATION STYLE
Burstall, F., Hertrich-Jeromin, U., & Lara Miro, M. (2019). Ribaucour coordinates. Beitrage Zur Algebra Und Geometrie, 60(1), 39–55. https://doi.org/10.1007/s13366-018-0391-9
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