Eikonal slant helices and Eikonal Darboux helices in 3-dimensional Riemannian manifold

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In 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.