Geodesic
Pedal curves of fronts in the sphere
Li, Yanlin1 ; Pei, Donghe1
1 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 3, p. 836-844.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio Math., 43 (2010), 447-459] 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.
DOI : 10.22436/jnsa.009.03.12
Classification : 51B20, 53B50, 53A35
Keywords: Pedal curve, front, singularity, Legendre curve.

Li, Yanlin 1 ; Pei, Donghe 1

1 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China 
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Li, Yanlin; Pei, Donghe. Pedal curves of fronts in  the sphere. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 3, p. 836-844. doi : 10.22436/jnsa.009.03.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.03.12/

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