(k,m)-type slant helices for partially null and pseudo null curves in Minkowski space 𝔼14{\rm{\mathbb E}}_1^4

Abstract

In this study we define the notion of (k,m)-type slant helices in Minkowski 4-space and express some characterizations for partially and pseudo null curves in {\rm{\mathbb E}}_1^4 .

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

“…The constant vector U is on axis of (k, m)-type slant helix [1,9]. We decompose U with respect to PTF T(t), N(t), B 1 (t), B 2 (t) .…”

“…M.Y. 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.…”

CHARACTERIZATION OF BI-NULL SLANT(BNS) HELICES OF (k,m )-TYPE IN R^3_1 AND R^5_ 2

“…Proceeding on, in [13] and [14], some characterizations were proved for bi null Cartan curves to be k-type slant helices in semi Euclidean spaces R 6 3 and R 5 2 respectively. Later in 2020, a class of slant helices called (k, m) type slant helices was considered in [3] which presented a study of (k, m) type slant helices for partially null and pseudo null curves in Minkowski space E 4 1 . The aim of this paper is to give characterization for bi null curve to be (k, m)type slant helices in R 5 2 using the curvature function.…”

“…The aim of this paper is to give characterization for bi null curve to be (k, m)type slant helices in R 5 2 using the curvature function. Moreover, characterizations of bi-null curves to be (k, m) type slant helix have also been obtained in R 3 1 with modified orthogonal frame.…”

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

“…Soliman et al [4] investigated the progression of space curves using the type 3-Bishop frame. Bektaş and Yılmaz [5,6] described (𝑘, 𝑚)-type slant helices in 𝔼 4 and null curves in 4dimensional Minkowski space.…”