DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE E₁³

Abstract

Abstract. In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space E 3 1 . Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in E 3 1 . As an example, the obtained results are applied to the case ρ = const. and k 2 = const., and are discussed.

An approximate solution of equations characterizing spacelike curves of constant breadth in minkowski 3-space

“…Similarly, an arbitrary curve − → α = − → α (s) locally be spacelike if all of its velocity − → α ′ (s) are spacelike [14].…”

“…Also Aydın [2] obtains differential equation characterizing curves of constant breadth in E n and then she obtains approximate solutions of this equation using Taylor matrix collocation method. Studies in different spaces [14,18] on these curves are going on nowadays, currently. These curves are used in the kinematics of machinary, engineering and com design.…”

Some characterizations of constant breadth curves in Euclidean 4-space

“…Moreover, constant breath curves have been studied in Minkowski space. Kazaz,Önder and Kocayigit have studied spacelike curves of constant breadth in Minkowski 4-space [10].Önder, Kocayigit and Candan have obtained and studied the differential equations characterizing constant breadth curves in Minkowski 3-space [15]. Furthermore, Kocayigit andÖnder have showed that constant breadth curves are normal curves, helices, and spherical curves in some special cases [11].…”

On the curves of constant breadth in four dimensional Galilean space

“…S. Yılmaz and M. Turgut expressed some characterizations of timelike curves of constant breadth in Minkowski 3-space and partially null curves of constant breadth in semi-Riemannian space in [14][15]. And recently this topic were studied in higher dimensions and further characterizations related to different geometries were obtained, see [1], [4], [6][7][8] and [11][12][13],S.Yılmaz (2010) defined Frenet-Serret frame in four dimensional Galilean Space,see [16].…”