Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Characterization of Involutes and Evolutes of a Given Curve in 𝔼n

  • Received : 2017.07.14
  • Accepted : 2018.02.08
  • Published : 2018.03.23
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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 ${\mathbb{E}}^n$. 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 ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

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References

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