Special helices on equiform differential geometry of spacelike curves in Minkowski space-time

Abstract

In this paper, we establish k-type helices for equiform di¤erential geometry of spacelike curves in 4-dimensional Minkowski space E 4 1. Also we obtain (k; m)-type slant helices for equiform di¤erential geometry of spacelike curves in Minkowski space-time. 2020 Mathematics Subject Classi…cation. 53A35. Keywords and phrases. Equiform Frenet frame, k-type helices, (k; m)-type slant helices.

(k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space

“…Yilmaz and M. Bektas ¸defined (k, m)-type slant helices in 4-dimensional Euclidean space and null curves in Minkowski 4-space [1,9]. In addition, F. Bulut and M. Bektas ¸ [3] obtained special helices on Equiform differential geometry of spacelike curves in Minkowski space-time. On the other hand, the Bishop frame was introduced by R. L. Bishop in 1975 utilizing parallel vector fields [2].…”

On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$

“…Additionally, Bulut and Bektaş [7] acquired particular helices upon isomorphic differential geometry of spacelike curves in Minkowski spacetime. Furthermore, Bükcü et al [8] investigated the spherical curves according to two types of modified orthogonal frames in 𝔼 3 .…”

On the Assocıated Curves of a Frenet Curve in R_1^4

“…Moreover, Bektaş, Ergüt and Öğrenmiş in [2] , mentioned a special curves of 4D Galilean space. Also, in [3] author introduced special helices on equiform differential geometry of time-like curves in 𝐸 . In [4][5], authors defined associated curves on different spaces and researched their applications.…”