Önder M.Ziplar E.Kaya O.2025-04-102025-04-102014http://hdl.handle.net/20.500.14701/49874In this study, we give the definitions and characterizations of Eikonal slant helices, Eikonal Darboux helices and non-modified Eikonal Darboux helices in 3-dimensional Riemannian manifold M3. We show that every Eikonal slant helix is also an Eikonal Darboux helix. Furthermore, we obtain that if the curve α is a non-modified Eikonal Darboux helix, then α is an Eikonal slant helix if and only if κ2 + τ2 = constant, where κ and τ are curvature and torsion of α, respectively. © World Scientific Publishing Company.Article10.1142/S0219887814500455