A SMARANDACHE CURVE ACCORDING TO THE DARBOUX FRAME AND THE KINEMATICS OF THIS CURVE IN MINKOWSKI SPACE

Abstract

In this study, the curvatures and frames of the Smarandache curve formed by a timelike curve with unit velocity taken on a timelike surface according to the Darboux frame in Semi-Euclidean space were created. Then, the image curve on the screw surface was obtained by applying translational and rotational motion (screw motion) using the quaternion multiplication under the same frame of this curve..Finally, the curvature and torsion of the obtained image curve were calculated