SLANT HELICES IN MINKOWSKI SPACE E₁³

Abstract

We consider a curve <TEX>$\alpha$</TEX>= <TEX>$\alpha$</TEX>(s) in Minkowski 3-space <TEX>$E_1^3$</TEX> and denote by {T, N, B} the Frenet frame of <TEX>$\alpha$</TEX>. We say that <TEX>$\alpha$</TEX> is a slant helix if there exists a fixed direction U of <TEX>$E_1^3$</TEX> such that the function <N(s)U> is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of <TEX>$\alpha$</TEX>. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in <TEX>$E_1^3$</TEX>.