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

Abstract

In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemannian manifold 3 M . We show that every eikonal slant helix is also an eikonal Darboux helix. , where κ and τ are curvature and torsion of α , respectively. MSC: 53A04, 14H45.