Direction curves of tangent indicatrix of a curve

Abstract

In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By using these associated curves, we give some methods to construct helices and slant helices from some special spherical curves such as circles on unit sphere, spherical helices, and spherical slant helices. Finally, we give some related examples.