Ribaucour coordinates

Francis Burstall, Udo Hertrich-Jeromin, Maria Lara Miro

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)39-55
Number of pages17
JournalBeitraege zur Algebra und Geometrie
Volume60
Issue number1
Early online date17 Apr 2018
DOIs
Publication statusPublished - 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

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