A Research on the Spherical Indicatrices of Directional Space Curve

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 33 - 39, 28.02.2020

Gül Uğur Kaymanlı Cumali Ekici Mustafa Dede

https://doi.org/10.18185/erzifbed.599336

Öz

In this paper, we give a parametrization of a directional space curve by using adapted frame called q-frame.. The spherical images of both directional normal indicatrix and directional tangent indicatrix of this space curve with q-frame are studied. Later using the geodesic curvature of the spherical image of the directional normal indicatrices, we work on the condition that a space curve to be slant helix. Finally, we give an application of the results.

Anahtar Kelimeler

q-frame, Slant helix, Spherical indicatrix

Yönlü Uzay Eğrisinin Küresel Göstergeleri Üzerine Bir Çalışma

Öz

Bu çalışmada, q-çatı olarak adlandırılan adapte edilmiş çatı kullanılarak yönlü uzay eğrisinin parametrik denklemini verdik. q-çatılı bu uzay eğrisinin Yönlü normaller ve teğetler göstergesinin küresel resimleri çalışıldı. Sonrasında yönlü normaller göstergelerinin küresel resminin jeodezik eğriliği kullanılarak uzay eğrisinin slant helis olma şartını çalıştık. Son olarakta, elde edilen sonuçların uygulaması verdik.

Anahtar Kelimeler

q-çatı, Slant helis, Küresel gösterge

Kaynakça

• Referans1 Ali, A.T. 2012. “New Special Curves and their Spherical Indicatrix”, Glob. J Adv. Res. Class. Mod. Geom., 1(2), 28-38.
• Referans2 Altunkaya, B. and Kula, L. 2016. “On Rectifying Slant Helices in Euclidean 3-Space”, Konuralp J. Math., 4(2), 17-24.
• Referans3 Bishop, R. L. 1975. “There Is More Than One Way to Frame a Curve”, Am. Math. Mon., 82(3), 246-251.
• Referans4 Bloomenthal, J. 1990. “Calculation of Reference Frames Along a Space Curve”, Graphics gems, Academic Press Professional Inc., San Diego, CA.
• Referans5 Bukcu, B. and Karacan, M.K. 2009. “The Slant Helices according to Bishop Frame”, Int. J. Comput. Math. Sci., 3, 67-70.
• Referans6 Chouaieb, N. Goriely, A. and Maddocks, J.H. 2006. “Helices”, PNAS, 103, 398-403.
• Referans7 Coquillart S. 1987. “Computing Offsets of B-Spline Curves”, Computer-Aided Design, 19(6), 305-09.
• Referans8 Dede, M. Ekici, C. and Görgülü, A. 2015. “Directional q-frame along a Space Curve”, IJARCSSE, 5, 775-780.
• Referans9 Dede, M. and Ekici, C. 2018. “Directional Bertrand Curves”, Gazi University Journal of Science, 31(1), 202-211.
• Referans10 Do Carmo, P.M. (1976). “Differential Geometry of Curves and Surfaces”, Prentice- Hall, Englewood Cliffs, New York.
• Referans11 Ekici, C. Dede, M. Tozak, H. 2017. “Timelike Directional Tubular Surfaces”, Int. J. Mathematical Anal., 8(5), 1-11.
• Referans12 Izumiya, S. and Tkeuchi, N. 2004. “New Special Curves and Developable Surfaces”, Turk. J. Math., 28, 153-163.
• Referans13 Kaymanlı, G. U. Ekici, C. Ekici and Dede, M. 2018. “Directional Canal Surfaces in E3”, Current Academic Studies in Natural Sciences and Mathematics Sciences, Ankara, 63-80.
• Referans14 Kula, L. Ekmekci, N. Yayli Y. and Ilarslan K. 2009. “Characterizations of Slant Helices in Euclidean 3-space”, Tur. J. Math., 33, 1-13.
• Referans15 Kula, L. and Yaylı, Y. 2005. “On Slant Helix and its Spherical Indicatrix”, Applied Mathematics and Computation, 169, 600-607.
• Referans16 Scofield, P.D. 1995. “Curves of Constant Precession”, Amer. Math. Monthly, 102, 531-537.
• Referans17 Shin, H. Yoo, S. K. Cho, S. K. Chung, W. H. 2003. “Directional Offset of a Spatial Curve for Practical Engineering Design”, ICCSA, 3, 711-720.
• Referans18 Wang, W. Jüttler, B. Zheng, D. and liu, Y. 2008. “Computation of Rotation Minimizing Frame”, ACM Trans. Graph, 27(1), 18 pages