A Smarandache Curve According to the Darboux Frame and the Kinematics of this Curve in Minkowski Space

Authors : Fatih Karaman, Ümit Ziya Savcı

Pages : 1-13

Doi:10.53508/ijiam.1311214

View : 74 | Download : 80

Publication Date : 2024-06-13

Article Type : Research Paper

Abstract :In this study, the curvatures and frames of the Smarandache curve formed by a unıt speed timelike curve taken on a time like surface according to Darboux frame in Semi-Euclidean space $\\mathbb{E}_1^3$ were created. Then, the image curve on the screw surface was obtained by applying translational and rotational motion using the quaternion multiplication under the same frame of this curve. Finally, the curvature and torsion of the obtained image curve were calculated.
Keywords : Smarandache Curve, Quaternon, Screw Surface, Image Curve