Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame

Abstract

In this study, the spherical indicatrices of Flc frame vectors were defined on unit sphere. The arc length parameters and the Frenet vectors of these indicatrix curves were calculated, as well. Last, we have provided the geodesic curvatures according to both Euclidean space E 3 and unit sphere S 2 .

On Ruled Surfaces Constructed by the Evolution of a Polynomial Space Curve

“…T X be a tangent ruled surface with the Flc frame, then the surface (11) where the curvatures 1 d and 3 d depend on the parameters s and t . By considering the partial derivatives of the surface 2 D X given by Eq (10) and Eq. ( 1), one can get the normal vector field of the normal-like ruled surface as:…”

“…To solve this problem, Dede defined the Flc frame for moving polynomial curves [7,8]. The Flc frame [9][10][11][12][13] and ruled surfaces on different frames [14][15][16][17][18][19][20][21][22][23] have been investigated by many researchers. Inspired by these studies, we conducted this research to create a new resource on the subject of surfaces and to form a basis for future studies.…”