New type directional curves of a curve in Minkowski 3-space

In this thesis, using the Darboux frame {T,ζ,η} instead of Frenet frame {T,N,B} in Minkowski 3-space E_1^3, the new associated curves are given as integral curves of vector fields D ̅_n, D ̅_r, and D ̅_o lying in the planes spanned by {ζ,η}, {T,η}, and {T,ζ} of the space-like curve α with space-like principal normal lying on a time-like surface M, respectively. Some relation between the Darboux frame and the curvatures k_g, k_n, τ_g of the curve α and the Frenet apparatus of the associated curves of α are obtained. Taking into consideration these relations, the necessary and sufficient conditions for the associated curves to be a helix and a spherical curve are given . Finally, some related examples are provided.