Publication: A characterization of involutes and evolutes of a given curve in En
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Öztürk, Günay
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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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Keywords
Curvatures, Vertices, Frenet curve, Involutes, Evolutes, Science & technology, Physical sciences, Mathematics