Evolutes of fronts on Euclidean 2-sphere
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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.
Share and Cite
ISRP Style
Haiou Yu, Donghe Pei, Xiupeng Cui, Evolutes of fronts on Euclidean 2-sphere, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 678--686
AMA Style
Yu Haiou, Pei Donghe, Cui Xiupeng, Evolutes of fronts on Euclidean 2-sphere. J. Nonlinear Sci. Appl. (2015); 8(5):678--686
Chicago/Turabian Style
Yu, Haiou, Pei, Donghe, Cui, Xiupeng. "Evolutes of fronts on Euclidean 2-sphere." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 678--686
Keywords
- framed curve
- evolute
- front.
MSC
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