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

作者：Langevin Remi^*; O' Hara Jun; Sakata Shigehiro

来源：Annales Polonici Mathematici, 2013, 108(2): 109-131.

DOI：10.4064/ap108-2-1

• Mobius geometry
• canal surface
• conformal arc-length
• conformal curvature
• conformal torsion
• osculating circle
• osculating sphere

We review some techniques from the Mobius 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 Mobius 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.

• 出版日期2013