DIFFERENT PERSPECTIVE OF DARBOUX SLANT RULED SURFACES AND THEIR CONSTRUCTIONS VIA QUATERNIONS

In this paper, based on the definition of Darboux slant ruled surface in IP3, a novel method for the Darboux slant ruled surface obtained from the striction curve of the natural lift curve is described in IP3. Then, an isomorphism between the unit dual sphere, TM, and the subset of the unit 2-sphere, is used to define this surface. Hence, the striction curve of the natural lift curve is corresponded to Darboux slant ruled surface in IP(3 )by considering the isomorphism. Additionally, some fundamental theorems are proved to characterize this surface. Using the quaternion product of the quaternionic operator and a pure unit quaternion, the quaternionic expression for the Darboux slant ruled surface is defined. In the last, 2-parameter homothetic motion is expressed for this surface.