Application of spaces of subspheres to conformal invariants of curves and canal surfaces

Rémi Langevin, Jun O'Hara, Shigehiro Sakata

Research output: Contribution to journalArticle

Abstract

We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows for the re-expression of the conformal invariants in terms of standard Euclidean invarian

Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalAnnales Polonici Mathematici
Volume108
Issue number2
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Canal surface
  • Conformal arc-length
  • Conformal curvature
  • Conformal torsion
  • Möbius geometry
  • Osculating circle
  • Osculating sphere

ASJC Scopus subject areas

  • Mathematics(all)

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