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The explicit determinations of dual plane curves and dual helices in terms of its dual curvature and dual torsion

Lee J. W., Choi J.H., Jin D. H.

Demonstratio Mathematica

2014

Vol. 47, nr 1

156--169

In this paper, we give the explicit determinations of dual plane curves, general dual helices and dual slant helices in terms of its dual curvature and dual torsion as a fundamental theory of dual curves in a dual 3-space.

Singularities of pedal curves produced by singular dual curve germs in Sn

Nishimura T.

Demonstratio Mathematica

2010

Vol. 43, nr 2

447-459

For an n-dimensional spherical unit speed curve r and a given point P, we can define naturally the pedal curve of r relative to the pedal point P. When the dual curve germs are singular, singularity types of pedal curves depend on singularity types of the n-th curvature function germs and the locations of pedal points. In this paper, we investigate sigularity types of pedal curves in such cases.