Revista Notas de Matemática Vol.7(1), No. 304, 2011, pp. 57-65 http://www.saber.ula.ve/notasdematematica Pre-prints Departamento de Matemáticas Facultad de Ciencias Universidad de Los Andes Special motions for spacelike curve in Minkowski 3-space Naser Masrouri and Yusuf Yayli Abstract Existence of acceleration pole points in special Frenet and Bishop motions for spacelike curve with a spacelike binormal in Minkowski 3-space E 3 1 are dependence into that, the curve α is not a general helix or planar. The ratio of torsion and curvature is by taking as a constant or non constant in our study. Then we show that, if the ratio of curvatures is constant, then there is not acceleration pole points of motion. AMS subject classifications. Primary 53A04; 53A17 1 Preliminaries Let R 3 be the real vector space with its usual vector structure. The Minkowski 3-space is the metric space E 3 1 =(R 3 , 〈, 〉 L ), where the metric 〈, 〉 L is given by 〈x, y〉 L = x 1 y 1 + x 2 y 2 − x 3 y 3 : x =(x 1 ,x 2 ,x 3 ),y =(y 1 ,y 2 ,y 3 ) The metric 〈, 〉 L is called the Lorentzian metric [4, 6]. A vector x ∈ E 3 1 is called: i) Spacelike if 〈x, x〉 L > 0 or x =0, ii) Timelike if 〈x, x〉 L < 0, iii) Null (lightlike) if 〈x, x〉 L =0 and x =0. Denote by {T,N,B} the moving Frenet frame and the moving Bishop frame along the regular curve α = α(t) that are parameterized by the length- arc parameter t The Frenet trihedron consists of the tangent vector T , the principle normal vector N and the binormal vector B, and the Bishop trihedron consists of the tangent vector T , the 1 st principle normal vector N 1 and 2 nd principle normal vector N 2 , which are three mutually orthogonal axes. 57