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

• Autorzy: Rémi Langevin , Jun O'Hara , Shigehiro Sakata
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53A30: Conformal differential geometry
• 53B50: Applications to physics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 108
• Numer: 2
• Strony: 109-131

Daty

wydano

2013

Twórcy

autor

Rémi Langevin

• Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne, 21078 Dijon, France

autor

Jun O'Hara

• Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan

autor

Shigehiro Sakata

• Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan

Identyfikatory

DOI

10.4064/ap108-2-1