Pedal curves of fronts in the sphere
Authors
Yanlin Li
 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China.
Donghe Pei
 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China.
Abstract
Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio
Math., 43 (2010), 447459] has done some work associated with the singularities of pedal curves of regular
curves. But if the curve has singular points, we can not define the Frenet frame at these singular points. We
also can not use the Frenet frame to define and study the pedal curve of the original curve. In this paper,
we consider the differential geometry of pedal curves of singular curves in the sphere. We define the pedal
curve of a front and give properties of such pedal curve by using a moving frame along a front. At last, we
give the classification of singularities of the pedal curves of fronts.
Keywords
 Pedal curve
 front
 singularity
 Legendre curve.
MSC
References

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