Al-Obaidi, Shaymaa S. A.Mahmood, Ghassan A. MahmoodÖztürk, Ufuk2024-09-252024-09-2520242357-2205https://doi.org/10.28924/APJM/11-29https://hdl.handle.net/20.500.12491/12871In this study, we explore new associated curves in Minkowski 3?space E31 by using the Darboux frame {T, ?, ?} instead of Frenet frame {T, N, B} of the spacelike curve ? having a spacelike principal normal lying on a timelike surface M. These associated curves, denoted as¯Dn,¯Dr, and¯Do, lie in planes defined by {?, ?}, {T, ?}, and {T, ?}, respectively. We establish relationships between the Darboux frame and the curvatures kg, kn, ?g of the curve ? as well as the Frenet apparatus of the associated curves. Furthermore, we derive necessary and sufficient conditions for these associated curves to exhibit helical or spherical characteristics. Finally, we present relevant examples. © 2024 Asia Pacific Journal of Mathematics.eninfo:eu-repo/semantics/openAccessassociated curveshelicesisophote curvesMinkowski 3?spacerelatively normal-slant helicesspacelike curvespherical curvesArticle10.28924/APJM/11-29112-s2.0-85186254255Q4