TY - JOUR T1 - Parallel Curves Based on Normal Vector TT - Normal Vektöre Dayalı Paralel Eğriler AU - Sağıroğlu, Yasemin AU - Köse, Gönül PY - 2024 DA - June DO - 10.33484/sinopfbd.1315640 JF - Sinop Üniversitesi Fen Bilimleri Dergisi JO - Sinop Uni J Nat Sci PB - Sinop Üniversitesi WT - DergiPark SN - 2536-4383 SP - 1 EP - 13 VL - 9 IS - 1 LA - en AB - 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. KW - Curves KW - Frenet frame KW - curvature KW - torsion N2 - 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. CR - 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 CR - 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 CR - 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 CR - İlarslan, K., & Nesovic, E. (2008). Some characterization of rectifying curves in the Euclidean Space E^4, Turkish Journal of Mathematics, 32, 21-30. CR - 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 CR - Sağıroğlu, Y. (2015). Global differential invariants of affine curves in R2. Far East Journal of Mathematical Sciences, 96(4), 497-515. CR - 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 CR - 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 CR - 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 CR - 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 CR - 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 CR - 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 CR - 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 CR - 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. CR - O’Neill, B. (2006). Elementary Differential Geometry, Revised Second Edition, Elsevier, USA. UR - https://doi.org/10.33484/sinopfbd.1315640 L1 - http://dergipark.org.tr/tr/download/article-file/3214445 ER -