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

Tom 108 / 2013

Rémi Langevin, Jun O'Hara, Shigehiro Sakata Annales Polonici Mathematici 108 (2013), 109-131 MSC: Primary 53A30; Secondary 53B50. DOI: 10.4064/ap108-2-1

Streszczenie

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 invariants.

Autorzy

  • Rémi LangevinInstitut de Mathématiques de Bourgogne
    UMR CNRS 5584
    Université de Bourgogne
    21078 Dijon, France
    e-mail
  • Jun O'HaraDepartment of Mathematics
    Tokyo Metropolitan University
    Tokyo 192-0397, Japan
    e-mail
  • Shigehiro SakataDepartment of Mathematics
    Tokyo Metropolitan University
    Tokyo 192-0397, Japan
    e-mail

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