On partially null and pseudo null curves in the semi-euclidean space $$ R^{4}_{2} $$

Abstract

In this paper, we obtain the Frenet equations of a pseudo null and a partially null curves, lying fully in the semi-Euclidean space R 4 2 , and classify all such curves with constant curvatures. (2000): 53C50, 53C40. Mathematics Subject Classification

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.…”

A Study on a Partially Null Curve in E₂⁴

“…) are …rst, second and third curvature of the curve , respectively. In the sequel, in [3] prove that k 3 (s) = 0 for each s. Consequently, there are only two curvatures k 1 (s) and k 2 (s) in this case. Thus, Frenet equations are as follows: 8 > > < > > :…”

“…; called angle between a and b, such that g(a; b) = kak kbk cos : We also recall that the pseudosphere S 3 2 and the pseudohyperbolic space H 3 1 are the hyperquadrics in E 4 2 ; de…ned respectively by:…”

“…Then T; N; B 1 ; B 2 are, respectively, the tangent, the principal normal ,the …rst binormal and the second binormal vector …elds. Recall that spacelike curve with timelike principal normal and a null …rst and second binormal is called a partially null curve in E 4 2 : Then for a partially null curve in E 4 2 ; the following Frenet equations are given in [3] 8 > > < > > :…”

A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴

“…Case 4. Let K be a unit speed partially lightlike curve K, then Frenet equations are stated as the following [17].…”