Spacelike and timelike normal curves in Minkowski space-time

Abstract

We define normal curves in Minkowski space-time E41. In particular, we characterize the spacelike normal curves in E41 whose Frenet frame contains only non-null vector fields, as well as the timelike normal curves in E41 , in terms of their curvature functions. Moreover, we obtain an explicit equation of such normal curves with constant curvatures.

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

“…For this purpose, the geometric characterization of the nonlightlike, pseudo lightlike, Cartan lightlike, and partially lightlike curves were characterized in by other works. () Considering the giving characterizations of the space curves of a distinct type, Körpınar and Demirkol determined the elasticity and nonelasticity conditions for them together with their energy.…”

On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds

“…Next, we investigate curves with null normals (for such curves in Minkowski spaces E 3 1 , see among others [2,7,8]). We say γ : I → M is a curve with null normal if g(γ,γ) = ε 1 = ±1 , ∇γγ = 0 , g(∇γγ, ∇γγ) = 0 .…”

Investigation of a curve using Frenet frame in the lightlike cone

“…Frenet frames are a centrical structure in modern differential geometry, in which construction is explained with regards to an object of interest rather than with regards to exterior coordinate systems. Many studies on curves using frenet frames have been reported by many mathematicians [6,7,[9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…More recently, besides in Euclidean space, many studies have been made in semi-Euclidean space: in [11] if the position vector of a curve always lies in its normal plane, this curve can be called a normal curve in Minkowski 3-space E 3 1 . Many studies related to spacelike, timelike and null normal curves, lying fully in the Minkowski 3-space, are given in [9][10][11][12][13]. Further, in [21], Yu and others define framed curves on Euclidean 2-sphere.…”