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New approach to timelike Bertrand curves in 3-dimensional Minkowski space
(Vasyl Stefanyk Precarpathian Natl Univ, 2023) Erdem, H. A.; Ucum, A.; İlarslan, K.; Camcı, Çetin
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 differ-ent 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.