A New Representation for Slant Curves in Sasakian 3-Manifolds

In this paper, we define a new kind of curve called N-slant curve whose principal normal vector field makes a constant angle with the Reeb vector field ξ in Sasakian $3$-manifolds. Then, we give some characterizations of N-slant curves in Sasakian $3$-manifolds and we obtain some properties of the curves in R³(-3). Moreover, we investigate the conditions of C-parallel and C-proper mean curvature vector fields along N-slant curves in Sasakian $3$-manifolds. Finally, we study N-slant curves of type $AW(k)$ where k=1,2 or 3.