Application of spaces of subspheres to conformal invariants of curves and canal surfaces
Volume 108 / 2013
Annales Polonici Mathematici 108 (2013), 109-131 MSC: Primary 53A30; Secondary 53B50. DOI: 10.4064/ap108-2-1
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.