Evolutes of fronts on Euclidean 2-sphere

Volume 8, Issue 5, pp 678--686 http://dx.doi.org/10.22436/jnsa.008.05.20

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Authors

Haiou Yu - School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China. - Department of Mathematical Education, College of Humanities and Sciences, Northeast Normal University, Changchun, 130117, P. R. China. Donghe Pei - School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China. Xiupeng Cui - School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China.

Abstract

We define framed curves (or frontals) on Euclidean 2-sphere, give a moving frame of the framed curve and define a pair of smooth functions as the geodesic curvature of a regular curve. It is quite useful for analysing curves with singular points. In general, we can not define evolutes at singular points of curves on Euclidean 2-sphere, but we can define evolutes of fronts under some conditions. Moreover, some properties of such evolutes at singular points are given.

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Keywords

• framed curve
• evolute
• front.

MSC

•  51B20
•  53B50
•  53A35

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