Torus Curves With Vanishing Curvature
Differential Geometry
2012-08-27 v1
Abstract
Let T be the standard torus of revolution in R^3 with radii b and 1, 0<b<1. Let \alpha be a (p,q) torus curve on T. We show that there are points of zero curvature on \alpha for only one value of the variable radius of T, b=p^2/(p^2+q^2). The curve \alpha has non-vanishing curvature for all other values of b. Moreover, for this value of b, there are exactly q points of zero curvature on \alpha.
Keywords
Cite
@article{arxiv.math/9803021,
title = {Torus Curves With Vanishing Curvature},
author = {Edgar J. Fuller,},
journal= {arXiv preprint arXiv:math/9803021},
year = {2012}
}
Comments
7 pages, 6 figures AMS-LaTeX with encapsulated postscript