In this paper, firstly, the ruled surface is expressed as a spatial
quaternionic. Also, the spatial quaternionic definitions of the Striction
curve, the distribution parameter, angle of pitch and the pitch are given.
Finally, integral invariants of the closed spatial quaternionic ruled
surfaces drawn by the motion of the Frenet vectors {t,n1,n2} belonging to
the spatial quaternionic curve ? are calculated.
In this paper, we found the Darboux vector of the spatial quaternionic curve according to the Frenet frame. Then, the curvature and torsion of the spatial quaternionic smarandache curve formed by the unit Darboux vector with the normal vector was calculated. Finally; these values are expressed depending upon the spatial quaternionic curve.
In this paper, when the Frenet vectors of the partner curve of Mannheim curve are taken as the position vectors, the curvature and the torsion of Smarandache curves are calculated. These values are expressed depending upon the Mannheim curve. Besides, we illustrate example of our main results.
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