The Quaternionic Expression of Ruled Surfaces

Abstract

In this paper, firstly, the ruled surface is expressed as a quaternionic. Later, the quaternionic definitions of the Striction curve, the distribution parameter, angle of pitch and the pitch in the closed ruled surface are given. Finally, integral invariants of the closed quaternionic ruled surfaces drawn by the motion of the Frenet vectors {t, n1, n2} belonging to the quaternionic curve α are calculated.