Some Characterizations of Spherical Indicatrix Curves Generated by Sannia Frame

Abstract

In this study, we have first provided the relations between the Frenet frame and Sannia frame on the striction points of four ruled surfaces of each formed by taking the basis as the tangent, normal, binormal and Darboux vector. Second, we have defined the relations between the Sannia vectors and their derivatives. For each Sannia frame, we have calculated the Darboux frame and expressed those in terms of Frenet frame. Last, we have obtained the arc lengths and the geodesic curvatures according to both Euclidean space E3 and unit sphere S2 of Sannia vectors for each four of ruled surfaces.