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

Yıl 2024, Cilt: 7 Sayı: 1, 1 - 13, 13.06.2024

Fatih Karaman , Ümit Ziya Savcı

https://doi.org/10.53508/ijiam.1311214

Öz

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.

Anahtar Kelimeler

Smarandache Curve, Quaternon, Screw Surface, Image Curve

Kaynakça

• Ahmad T Ali. Special smarandache curves in the euclidean space. International Journal of Mathematical Combinatorics, 2:30{36, 2010.
• Fatih Karaman.  Ozel smarandache egrileri. Master's thesis, Bilecik Seyh Edebali Universitesi, Fen Bilimleri Enstitusu, 2015.
• Ozcan Bektas and Salim Yuce. Special smarandache curves according to darboux frame in e3. arXiv preprint arXiv:1203.4830, 2012.
• M Khalifa Saad. Spacelike and timelike admissible smarandache curves in pseudogalilean space. Journal of the Egyptian Mathematical Society, 24(3):416{423, 2016.
• EM Solouma. Special equiform smarandache curves in minkowski space-time. Jour- nal of the Egyptian Mathematical Society, 25(3):319{325, 2017.