K-type slant helices on spacelike and timelike surfaces

Abstract

We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E₁³, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.