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A characterization of involutes and evolutes of a given curve in En

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2018-03-01

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Kyungpook Natl Univ, Dept Mathematics

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Abstract

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space E-n. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space E-n. Further, we obtain some results on these type of curves in E-3 and E-4, respectively.

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Curvatures, Vertices, Frenet curve, Involutes, Evolutes, Science & technology, Physical sciences, Mathematics

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