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

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 M-3. We show that every Eikonal slant helix is also an Eikonal Darboux helix. Furthermore, we obtain that if the curve a is a non-modified Eikonal Darboux helix, then a is an Eikonal slant helix if and only if K-2 + T-2 = constant, where K and T are curvature and torsion of alpha, respectively.