Normal Vektöre Dayalı Paralel Eğriler

Yıl 2024, Cilt: 9 Sayı: 1, 1 - 13, 29.06.2024

Yasemin Sağıroğlu , Gönül Köse

https://doi.org/10.33484/sinopfbd.1315640

Cited By: 2

https://izlik.org/JA33GS85RB

Öz

Bu çalışmada, normal vektöre dayalı paralel eğrilerin tanımı verilmiş ve bu eğrinin eğriliği, burulması, Frenet çatısı belirlenmiştir. Ayrıca, çember ve helis gibi eğrilerdeki özel durumlar da örneklendirilmiştir.

Anahtar Kelimeler

Eğri , Frenet çatısı , eğrilik , burulma

Parallel Curves Based on Normal Vector

https://izlik.org/JA33GS85RB

Öz

In this paper, the definition of parallel curves based on normal vector is given and the curvature, torsion, Frenet frame of this curve are determined. Furthermore, special cases in curves such as circle and helix are also be exemplified.

Anahtar Kelimeler

Curves , Frenet frame , curvature , torsion

Kaynakça

• Arslan, K., & Hacısalihoğlu, H. H. (2000). On harmonic curvatures of a frenet curve. Communications De La Faculte des Sciences de L’Universite D’Ankara”, 49, 015-023. https://doi.org/10.1501/Commua1_0000000374
• Ergin, A. A. (1992). On the generalized darboux curves, Communications De La Faculte des Sciences de L’Universite D’Ankara”, 41, 073-077. https://doi.org/10.1501/Commua1_0000000499
• Liu, H., & Wang, F. (2008). Mannheim partner curves in 3-space. Journal of Geometry, 88(1-2), 120-126. https://doi.org/10.1007/s00022-007-1949-0
• İlarslan, K., & Nesovic, E. (2008). Some characterization of rectifying curves in the Euclidean Space E^4, Turkish Journal of Mathematics, 32, 21-30.
• Has, A., & Yılmaz, B. (2022). On quaternionic bertrand curves in euclidean 3-space. Turkish Journal of. Mathematics and Computer Science, 14(2), 355-365. https://doi.org/10.47000/tjmcs.1021801
• Sağıroğlu, Y. (2015). Global differential invariants of affine curves in R2. Far East Journal of Mathematical Sciences, 96(4), 497-515.
• Divjak, B. (2003). Special curves on ruled surface in galilean and pseudo-galilean space. Acta Mathematica Hungarica, 98(3), 203-215. https://doi.org/10.1023/A:1022821824927
• Bükcü, B., & Karacan, M. K. (2008). Bishop frame of the spacelike curve with a spacelike principal normal in minkowski 3-space. Communications De La Faculte des Sciences de L’Universite D’Ankara”, 57(1), 13-22. https://doi.org/10.1501/Commua1_0000000185
• Şenyurt, S., Canlı, D., & Ayvacı, K. H. (2022). Associated curves from a different point of view in E^3. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(3), 826-845. https://doi.org/10.31801/cfsuasmas.1026359
• Güler, F. (2022). The quasi parallel curve of a space curve. Celal Bayar University Journal of Science, 18(2), 203-206. https://doi.org/10.18466/cbayarfbe.955974
• Srivastava, A., Klassen, E., Shantanu, H. J., & Jermyn, I. H. (2011). Shape analysis of elastic curves in euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(7), 1415-1428. https://doi.10.1109/TPAMI.2010.184
• Sanchez-Reyes, J. (2015). Detecting symmetries in polynomial B´ezier curves. Journal of Computational and Applied Mathematics, 288, 274-283. https://doi.org/10.1016/j.cam.2015.04.025
• Gözütok, U., Çoban, H. A., & Sağıroğlu, Y. (2019). Frenet frame with respect to conformable derivative. Filomat, 33(6), 1541-1550. https://doi.org/10.2298/FIL1906541G
• Aldossary, M., T., & Gazwani, M. A. (2020). Motion of parallel curves and surfaces in euclidean 3-space R^3. Global Journal of Advanced Research on Classical and Modern Geometries, 9(1), 43-56.
• O’Neill, B. (2006). Elementary Differential Geometry, Revised Second Edition, Elsevier, USA.