Characterizations of The Ruled Surfaces due to N-Bishop Frame

Year 2022, , 113 - 134, 15.06.2022

Hatice Kusak Samancı , Mustafa Sevinç

https://doi.org/10.31466/kfbd.937683

Cited By: 3

Abstract

In this study, a new ruled surface was defined by using the elements of the N-Bishop frame as a directed vector and the integral curve of the principal normal as a base curve. Then, the differential geometric properties of this new ruled surface such as distribution parameter, striction curve, Gaussian and mean curvature were examined. At the end of the work, various examples were presented related to this new ruled surface.

Keywords

Ruled surfaces, Serret-Frenet frame, N-Bishop frame

N-Bishop Çatısına Göre Regle Yüzeylerin Bazı Karakterizasyonları

Abstract

Bu çalışmada, doğrultmanı N-Bishop çatısının elemanlarından ve dayanak eğrisi ise asli normalinin integral eğrisinden oluşan yeni bir regle yüzey tanımlaması yapılmıştır. Daha sonra, tanımlanan bu yeni regle yüzeyin dağılma parametresi, sitriksiyon çizgisi, Gauss ve ortalama eğriliği gibi diferansiyel geometrik özellikleri incelenmiştir. Çalışmanın sonunda ise bu yeni regle yüzey ile ilgili çeşitli örnekler verilmiştir.

Keywords

Regle yüzeyleri, Serret-Frenet çatısı, N-Bishop çatısı.

References

• Andaras,C., Recio,T., Tabera, L.F., Sendra, J.R., Villarino,C., (2011), Proper real reparametrization of rational ruled surfaces. Comput. Aided Geom. Des., 28(2), 102-113.
• Bishop, R. L. (1975). There is more than one way to frame a curve. Am. Math. Mon., 82(3), 246-251.
• Bottema O.,Roth B., (1979). Theoretical kinematics, North-Holland Publishing Company, New York, p.558.
• Çalışkan A., Şenyurt S., (2018). Curves and ruled surfaces according to alternative frame in dual space. Commun. Fac.Sci.Univ. Ank.Ser.A1 Math.Stat., 69 (1), 684-698.
• Damar. E., Yuksel, N., Vanlı, T.A., (2017), The ruled surfaces according to type-2 Bishop frame in Int. Math. Forum, 2(12), No.3, 133-143.
• Hacısalihoğlu, H.H., (1983), Diferansiyel geometri II. Gazi Üniversitesi Yayınları.
• Keskin, O., Yaylı, Y., (2017), An application of N-Bishop frame to spherical images for direction curves. Int. J. Geom. Methods Mod. Phys., 14(11).
• Kılıçoğlu, Ş., Hacısalihoğlu, H.H., (2013). On the ruled surfaces whose frame is the Bishop frame in the Öklidean 3-space. Int. Electron. J. Geom., 6(2), 110-117.
• Kuşak Samancı H., (2020). N-Bishop Darboux vector of a timelike curve in Minkowski 3 Space. Journal of Science and Arts, 3(52), 519–528.
• Masal, M., Azak, A., (2019). Ruled surfaces according to Bishop frame in the Öklidean 3-spaces. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 89(2), 415-424.
• Ouarab, S., Ouazzani, A., Izıd, M. (2018). Ruled surfaces with alternative moving frame in Öklidean 3-space. International J. of Math. Sci. & Engg. Appls.(IJMSEA), 43-58.
• Scofield, P.D., (1995), Curves of constant precessions. Amer. Math. Monthly, 102(6), 531-537.
• Senturk, G.Y., Yuce, S., (2015), Characteristic properties of the ruled surface with Darboux frame In Kuwait J. Sci., 42(2), 14-33.
• Şahiner B. (2019) Ruled surfaces according to alternative moving frame, arXiv:1910.06589.
• Uzunoğlu, B., Gök, I.,Yaylı, Y., (2016), A New approach on curves of constant precession. Appl. Math. Comput., 275, 317-323.
• Yaylı, Y., Saraçoğlu, S., (2012). Different approaches to ruled surfaces. SDU Journal of Science, 7(1), 56-58.
• Yılmaz, B., Ramis, Ç., Yaylı, Y., (2017). On developable ruled surface of the principal direction curve. Konuralp Journal of Mathematics, 5(2), 172-180.
• Yüksel, N.,Vanlı, A.T., Damar, E., (2015) 3-boyutlu Öklidyen uzayda Bishop çatılı DNA ve regle yüzeyler. Doktora Tezi, Erciyes Üniversitesi, Kayseri.