3-Boyutlu Öklid Uzayında Adjoint Eğrilerin Binormal Yüzeyleri

Bu çalışmada, bağlantılı eğriler yardımıyla tanımlanmış geniş uygulama alanlarına sahip yüzeyler konusuna kendine has bir katkı sunuyoruz. Özelde, bağlantılı eğrilerin önemli örneklerinden biri olan adjoint eğriler ile oluşturulan binormal yüzeyleri inceliyoruz. 3-boyutlu Öklid uzayında Frenet-Serret (FS) çatısı altında adjoint eğrilerin binormal yüzeylerini tanımlayarak, böyle yüzeyleri karakterize ediyoruz. Bu karakterizasyonlar yardımıyla bazı sonuçlar veriyoruz.

Anahtar Kelimeler:

Binormal yüzey, Adjoint eğri, Frenet-Serret çatı

Binormal Surfaces of Adjoint Curves in 3D Euclidean Space

In this study, we make a specific contribution to the subject of surfaces with wide application areas defined with the help of associated curves. In particular, we examine the binormal surfaces generated via adjoint curves which are one of the important examples of associated curves. By defining the binormal surfaces of adjoint curves under the Frenet-Serret (FS) frame in 3D Euclidean space, we characterize such surfaces and give some results with the aid of these characterizations.

Keywords:

Binormal surface, Adjoint curve, Frenet-Serret frame,

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[1] Do Carmo M., “Differential Geometry of Curves and Surfaces”, Prentice-Hall, Englewood Cliffs, (1976).
[2] Nurkan S. K., Güven I. A. and Karacan M. K., “Characterizations of adjoint curves in Euclidean 3-space”, Proc Natl Acad Sci. India Sect A Phys Sci., 89: 155-161, (2019).
[3] Kaymanli G. U., Okur S. and Ekici C., “The Ruled Surfaces Generated By Quasi Vectors”, IV. International Scientific and Vocational Studies Congress - Science and Health, November, (2019).
[4] Lopez R., “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, MiniCourse taught at IME-USP, Brasil, (2008).
[5] Dreibelbis D., “Singularities of the Gauss map and the binormal surface”, Adv. Geom., 3: 453-468, (2003).
[6] Lopez R., Sipus Z. M., Gajcic L. P., Protrka I., “Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz-Minkowski space”, International Journal of Geometric Methods in Modern Physics, 16(5), (2019).
[7] Aydemir I. and Orbay K. “The Ruled Surfaces Generated By Frenet Vectors of Timelike Ruled Surface in the Minkowski Space R_1^3”, World Applied Science Journal, 6(5): 692-696, (2009).
[8] Protrka I., “Harmonic Evolutes of Timelike Ruled Surfaces in Minkowski Space”, 18th Scientific-Professional Colloquium on Geometry and Graphics, September, (2015).
[9] Protrka I., “The harmonic evolute of a helicoidal surfaces in Minkowski 3-space”, Proceedings of the Young Researcher Workshop on Differential Geometry in Minkowski Space, Granada, Spain, 133-142, (2017).
[10] Sarıoglugil A. and Tutar A., “On Ruled Surface in Euclidean Space E_ ^3”, Int. J. Contemp. Math. Sci., 2(1): 1-11, (2007).
[11] Kühnel W., “Ruled W-surfaces”, Arch. Math. (Basel), 62: 475-480, (1994).
[12] Ünlütürk Y. and Ekici C., “Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in Minkowski 3-space”, New Trends in Mathematical Sciences, 1(1): 85-92, (2013).
[13] Karadağ H. B., Kılıç E. and Karadağ M., “On the developable ruled surfaces Kinematically generated in Minkowski 3-Space”, Kuwait Journal of Science, 41(1): 21-34, (2014).
[14] Altın M., Kazan A. and Karadağ H. B., “Ruled surfaces in E3 with density”, Honam Mathematical Journal, 41(4): 683-695, (2019).
[15] Senturk G. Y. and Yuce S., “Characteristic properties of the ruled surface with Darboux frame in E^3”, Kuwait J. Sci., 42(2): 14-33, (2015).
[16] Choi J. H. and Kim Y. H., “Associated curves of a Frenet curve and their applications”, Appl. Math. Comput., 218 (18): 9116-9124, (2012).
[17] Körpınar T., Sarıaydın M.T., and Turhan E., “Associated curves according to Bishop frame in Euclidean 3-space”, Adv. Model. Optim., 15(3): 713-717, (2013).
[18] Macit N. and Düldül M., “Some new associated curves of a Frenet curve in E3 and E4”, Turkish J. Math., 38: 1023-1037, (2014).
[19] Yılmaz S., “Characterizations of some associated and special curves to type-2 Bishop frame in E^3”, Kırklareli University J. Eng. Sci., 1: 66-77, (2015).
[20] Karadağ M. and Sivridağ A.İ., “On a Study of the Quaternionic Lorentzian Curve”, Journal of Polytechnic, 21(4): 937-940, (2018).
[21] Gündüz H., Kazan A. and Karadağ H.B., “Rotational surfaces generated by cubic hermitian and cubic bezier curves”, Journal of Polytechnic, 22(4): 1075-1082, (2019).
[22] Karadağ M., “A New Approach for the Pseudo-Quaternionic Lorentzian Evolute and Involute Curves”, Journal of Polytechnic, 1(1): 1-7, (2021).