English

Space of subspheres and conformal invariants of curves

Differential Geometry 2016-03-21 v1

Abstract

A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in the Minkowski space, which can naturally produce the conformal invariants and the normal form of the curve. We also give characterization of canal surfaces in terms of curves in the set of circles.

Keywords

Cite

@article{arxiv.1102.0344,
  title  = {Space of subspheres and conformal invariants of curves},
  author = {R. Langevin and J. O'Hara and S. Sakata},
  journal= {arXiv preprint arXiv:1102.0344},
  year   = {2016}
}

Comments

14pages