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Characterizations of slant helices in Euclidean 3-space
(Scientific Technical Research Council Turkey-Tubitak, 2010) Kula, L.; Ekmekci, N.; Yayli, Y.; Ilarslan, K.
In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a. space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.
New approach to timelike Bertrand curves in 3-dimensional Minkowski space
(Vasyl Stefanyk Precarpathian Natl Univ, 2023) Erdem, H. A.; Ucum, A.; Ilarslan, K.; Camci, C.
In the theory of curves in Euclidean 3-space, it is well known that a curve /3 is said to be a Bertrand curve if for another curve /3* there exists a one-to-one correspondence between /3 and /3* 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.