A Characterization of Involutes and Evolutes of a Given Curve in E-n


Ozturk G., ARSLAN K. , BULCA B.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.58, no.1, pp.117-135, 2018 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.5666/kmj.2018.58.1.117
  • Title of Journal : KYUNGPOOK MATHEMATICAL JOURNAL
  • Page Numbers: pp.117-135
  • Keywords: Frenet curve, involutes, evolutes, CURVATURES, VERTICES

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.