3-Boyutlu Öklid Uzayında 3-Tipinde Bishop Çatısına Göre Regle Yüzeyler

Yıl 2025, Cilt: 6 Sayı: 2, 288 - 299, 29.11.2025

Anıl Altınkaya

https://doi.org/10.63716/guffd.1762272

Öz

Bu çalışmada, ilk olarak, Öklid uzayında 3-tipinde Bishop çatısına göre regle yüzeyler tanımlanmıştır. Daha sonra bu yüzeylerin singülerliği, açılabilirliği ve striksiyon eğrileri elde edilmiştir. Sonrasında bu yüzeylerin Gauss ve ortalama eğrilikleri elde edildikten sonra minimal olma durumları incelenmiştir. Son olarak da, yüzeylerin dayanak eğrisinin 3-tipinde Bishop çatısına göre jeodezik eğri, asimptotik eğri ve eğrilik çizgisi olma durumları incelenmiş ve bulunan sonuçlar bir örnekle desteklenerek yüzey çizimleri MATLAB programı ile yapılmıştır.

Anahtar Kelimeler

Regle Yüzey , 3-Tipinde Bishop Çatısı , Öklidyen Uzay

Kaynakça

• Do Carmo, M. P. (1976). Differential Geometry of Curves and Surfaces. Prentice Hall Inc. Englewood Cliffs. New Jersey.
• Ergün, E. and Çalışkan, M. (2015). Ruled Surface Pair Generated By Darboux Vectors of a Curve and Its Natural Lift in R^3. Bulletin of Mathematics and Statistics Research, 3(2), 125-134.
• Masal, M. and Azak, A. Z. (2015). The ruled surfaces according to type-2 Bishop Frame in the Euclidean 3-space. Mathematical Sciences and Applications E-Notes, 3(2), 74-83.
• Mert, T. and Atçeken, M. (2021). Some Special Ruled Surfaces in Hyperbolic 3-Space, Konuralp Journal of Mathematics, 9(2), 298-309.
• Karaca, E. (2022). Singularities of the ruled surfaces According to RM Frame and Natural Lift Curves, Cumhuriyet Science Journal, 43(2), 308.
• Oztemir, Y. and Çalışkan, M. (2023). Intersections of ruled surfaces corresponding to curves on pseudo spheres in dual space, Journal of Science and Arts, 62, 61-76.
• Boyacıoğlu Kalkan, Ö. and Şenyurt, S. (2024). Osculating Type Ruled Surfaces with Type-2 Bishop Frame in E^3. Symmetry, 16, 498.
• Li, Y., Eren, K. and Ersoy, S. (2023). On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space. AIMS Mathematics, 8(9): 22256-22273. doi: 10.3934/math.20231135
• Li, Y., Eren, K., Ayvacı, K. H. and Ersoy, S. (2022). Simultaneous characterizations of partner ruled surfaces using Flc frame. AIMS Mathematics, 7(11): 20213-20229. doi: 10.3934/math.20221106
• Eren K., Kosal, H.H. (2020). Evolution of Space Curves and the Special Ruled Surfaces with Modified Orthogonal Frame, AIMS Mathematics, 5(3), 2027– 2039.
• Şaffak Atalay, G. (2025). On the characterisations of ruled surface pairs according to the Sabban frame. Filomat, 39:11, 3705–3717.
• Şaffak Atalay, G. (2025). Smarandache Curved Ruled Surfaces and Their Characterizations According to Modified Orthogonal Frame in E3. Applications and Applied Mathematics: An International Journal (AAM), Vol. 20, Issue 1, 19 pages.
• Bishop, L. R. (1975). There is more than one way to frame a curve. American Mathematical Monthly 3(2), 82.
• Yılmaz, S. and Turgut, M. (2010). A new version of Bishop frame and an application to spherical images. Journal of Mathematical Analysis and Applications, 371, 764-776.
• Al-Jedani, A. and Abdel-Baky, R. A. (2023). Sweeping Surfaces according to Type-3 Bishop Frames in Euclidean 3-Space. Symmetry, 15, 855.
• Sharief, D., Bang, Y.C. and Azeb, A. (2018). Natural mates of Frenet curves in Euclidean 3-space. Turkish Journal of Mathematics, 42, 2826–2840.
• O’Neill, B. (1966). Elementary Differential Geometry, Academic Press New York and London, 42-187.