Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 39-55 |
| Number of pages | 17 |
| Journal | Beitraege zur Algebra und Geometrie |
| Volume | 60 |
| Issue number | 1 |
| Early online date | 17 Apr 2018 |
| DOIs | |
| Publication status | Published - 31 Mar 2019 |
Keywords
- Canal surface
- Channel surface
- Circular net
- Curvature line net
- Discrete principal net
- Ribaucour coordinates
- Ribaucour transformation
- Semi-discrete surface
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
