Ruled Surfaces With W-direction Curves

Yıl 2020, Cilt: 7 Sayı: 1, 21 - 33, 28.06.2020

İlkay Güven

https://doi.org/10.35193/bseufbd.669840

Öz

In this study, some special ruled surfaces were determined which were constituted by using the base curve as the W-direction curves of a Frenet curve. We gave the characterizations of developability and minimality of these ruled surfaces. We investigated the relation between the primary curve and the base curve of ruled surfaces, we also inquired the occurence geodesic curve, asymptotic line and principal line of the W-direction curve on the ruled surface. Terminally, some examples were given.

Anahtar Kelimeler

Ruled surface, W-direction curve, Asymptotic curve, Geodesic curve, Line of curvature

W-Yönlü Eğrilerden Elde Edilen Regle Yüzeyler

Öz

Bu çalışmada, bir Frenet eğrisinin W-yönlü eğrisi dayanak eğrisi olarak kullanılıp elde edilen bazı özel regle yüzeyler tanımlanmıştır. Bu regle yüzeylerin açılabilirlik ve minimallik karakterizasyonlarını verdik. Esas eğri ve regle yüzeyin dayanak eğrisi arasındaki ilişkiyi, dayanak eğrisinin geodezik eğri, asimptotik eğri ve eğrilik çizgisi olması açısından inceledik. Ayrıca bazı örnekler de verildi.

Anahtar Kelimeler

Regle yüzey, W-yönlü yüzey, Asimptotik eğri, Geodezik eğri, Eğrilik çizgisi

Kaynakça

• Choi, J. H., & Kim, Y. H. (2012). Associated curves of a Frenet curve and their applications. Applied Math. And Comp., 218, 9116-9124.
• Choi, J. H., Kim, Y. H., & Ali, A. T. (2012). Some associated curves of Frenet nonlightlike curves in E13. Journal of Math. Anal. Appl., 394, 712-723.
• Do Carmo, M. P. (1976). Differential Geometry of Curves and Surfaces. Prentice-Hall Inc., New Jersey.
• Gray, A. (1993). Modern Differential Geometry of Curves and Surfaces with Mathematica 2nd ed. Boca raton, Fl: Crc Press.
• Izumiya, S., & Takeuchi, N. (2003). Special curves and ruled surfaces. Beitrage zur Alg. Und Geo., Contributions to Alg. And Geo., 44(1), 203-212.
• Izumiya, S., & Takeuchi, N. (2004). New special curves and developable surfaces. Turk. J. of Math., 28, 153-163.
• Kızıltuğ, S., & Önder, M. (2015). Associated curves of Frenet curves in three dimensional compact Lie group. Miskolc Mathematical Notes, 16(2), 953-964.
• Körpınar, T., Sarıaydın, M. T., & Turhan, E. (2013). Associated curves according to Bishop frame in Euclidean 3-space. Adv. Modelling and Optimization, 15, 713-717.
• Kula, L., & Yaylı, Y. (2005). On slant helix and spherical indicatrix. Applied Math. and Comp., 169, 600-607.
• Macit, N., & Düldül, M. (2014). Some new associated curves of a Frenet curve in E2 and E4 . Turk J. Math., 38, 1023-1037.
• O’neill, B. (2006). Elementary Differential Geometry. Academic Press.
• Scofield, P. D., (1995). Curves of constant precession. American Mathematical Monthly, 102(6), 531-537.
• Yu, Y., Liu, H., & Jung, S. D. (2014). Structure and characterization of ruled surfaces in euclidean 3-space. Applied Math. and Comp., 233, 252-259.