Space of subspheres and conformal invariants of curves
Abstract
A space curve is determined by conformal arclength, conformal curvature, and conformal torsion, up to Möbius 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2011
 arXiv:
 arXiv:1102.0344
 Bibcode:
 2011arXiv1102.0344L
 Keywords:

 Mathematics  Differential Geometry;
 53A30;
 53B30
 EPrint:
 14pages