New approach to timelike Bertrand curves in 3-dimensional Minkowski space


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Erdem H., Uçum A., İlarslan K., CAMCI Ç.

Carpathian Mathematical Publications, vol.15, no.2, pp.482-494, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.15330/cmp.15.2.482-494
  • Journal Name: Carpathian Mathematical Publications
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.482-494
  • Keywords: Cartan null curve, Minkowski 3-space. Bertrand curve, spacelike curve, timelike curve
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

In the theory of curves in Euclidean 3-space, it is well known that a curve β is said to be a Bertrand curve if for another curve β⋆ there exists a one-to-one correspondence between β and β⋆ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Minkowski 3-space. Related examples that meet these conditions are given. Moreover, thanks to this new approach, timelike, spacelike and Cartan null Bertrand mates of a timelike general helix have been obtained.