Quasi-Focal Curves of Spacelike Adjoint Curves in 3D Minkowski Space

Yıl 2022, Cilt: 26 Sayı: 3, 523 - 529, 30.06.2022

Talat Körpınar , Ahmet Sazak

https://doi.org/10.16984/saufenbilder.1063526

Öz

Associated curves bring meaningful geometric expression to the physics and mathematics fields in the characterization of curves and surfaces created by those curves, their behavior, and the study of particle motion in space-time. In this work, we examine the relationship between adjoint curves and focal curves, which are two important examples of associated curves. We do this review for spacelike curves under quasi(q)-frame in 3D Minkowski space. To put it more clearly, we obtain some new characterizations by defining the focal curve of the adjoint curve of a spacelike curve in this space.

Anahtar Kelimeler

quasi-frame, spacelike curve, focal curve, adjoint curve

Kaynakça

• [1] J. M. Lee, “Introduction to Smooth Manifolds”, Graduate Texts in Math., New York, 2003.
• [2] J. H. Choi and Y. H. Kim, “Associated curves of a Frenet curve and their applications”, Appl. Math. Comput., vol. 218, no. 18, pp. 9116-9124, 2012.
• [3] T. Körpınar, M. T. Sarıaydın, and E. Turhan, “Associated curves according to Bishop frame in Euclidean 3-space”, Adv. Model. Optim., vol. 15, no. 3, pp. 713-717, 2013.
• [4] N. Macit and M. Düldül, “Some new associated curves of a Frenet curve in E3 and E4”, Turkish J. Math., vol. 38, pp. 1023-1037, 2014.
• [5] S. Enghardt, J. Bauch, “Application of Focal Curves to the Evaluation of Conic Diffraction Lines”, Journal of Applied Mathematics and Physics, vol. 3, pp. 1386-1390, 2015.
• [6] S. Yılmaz, “Characterizations of some associated and special curves to type-2 Bishop frame in E^3”, Kırklareli University J. Eng. Sci., vol. 1, pp. 66-77, 2015.
• [7] R. Uribe-Vargas, “On vertices, focal curvatures and differential geometry of space curves”, Bull. Brazilian Math. Soc. vol. 36, no. 3, pp. 285-307, 2005.
• [8] S. Desmukh, B. Y. Chen and A. Alghanemi, “Natural mates of Frenet curves in Euclidean 3-space”, Turk. J. Math, vol. 42, pp. 2826-2840, 2018.
• [9] S. K. Nurkan, I. A. Güven and M. K. Karacan, “Characterizations of adjoint curves in Euclidean 3-space”, Proc Natl Acad Sci. India Sect A Phys Sci., vol. 89, pp. 155-161, 2019.
• [10] P. Alegre, K. Arslan, A. Carriazo, C. Murathan and G. Öztürk, “Some Special Types of Developable Ruled Surface”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 3, pp. 319-325, 2010.
• [11] T. Körpinar, H. Öztekin, “A Note on Quasi Biharmonic Curves According to Quasi Frame in the Minkowski Space”, Journal of Advanced Physics, vol. 7, pp. 1-3, 2018.
• [12] M. Dede, C. Ekici, and A. Görgülü, “Directional q-frame Along a Space Curve”, IJARCSSE, vol. 5, no. 12, pp. 775-780, 2015.
• [13] G. Tarım, “Minkowski Uzayında Yönlü Eğriler Üzerine”, Postgraduate Thesis, Eskişehir Osmangazi University, December 2016.