Curves and ruled surfaces according to alternative frame in dual space

Abstract

In this paper, the vectorial moments of the alternative vectors are expressed in terms of altrenative frame. According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to the (b N); (b C); (c W) dual curves are given. The integral invariants of these surfaces are computed and illustrated by presenting with examples.

Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces

“…He categorizes the ruled and the translation surfaces [19]. Some authors give crucial results about the curves and surfaces in different spaces [12,15,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. We can find more motivations of our work from some articles (see [38][39][40][41][42][43][44][45][46][47][48][49][50]).…”