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


ÖZTÜRK 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

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.