Araştırma Makalesi
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Directional Evolution of the Ruled Surfaces via the Evolution of Their Directrix Using q-frame along a Timelike Space Curve

Yıl 2020, Sayı: 20, 392 - 396, 31.12.2020
https://doi.org/10.31590/ejosat.681674

Öz

In this study, the ruled surfaces obtained by normal and binormal vectors along a timelike space curve in 3 dimensional Minkowski space by using q-frame is investigated. Directional evolutions of both quasi normal and quasi binormal ruled surfaces are studied by using their directrices. Then, we work on some geometric properties such as inextensibilty, developability and minimality of these ruled surfaces.

Kaynakça

  • H. N. Abd-Ellah, Evolution of translation Surfaces in Euclidean 3 space Applied Mathematics and Information Science. 9(2), 661-668, 2015.
  • K. Akutagawa and S. Nishikawa, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J. 42(2): 67-82, 1990.
  • R. Balakrishnan, R. Blumenfeld, (1997). Transformation of general curve evolution to a modified Belavin-Polyakov equation. J. Math. Phys., 38(11), 5878-5888.
  • M. Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Saddle River, 1976.
  • S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6): 305-09, 1987.
  • M. Dede, C. Ekici and A. Görgülü, Directional q-frame along a space curve, IJARCSSE. 5(12), 775-780, 2015.
  • M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra. 9(12), 527-535, 2015.
  • M. Dede, G. Tarım and C. Ekici, Timelike directional Bertrand curves in Minkowski Space, 15th International Geometry Symposium, Amasya, Turkey 2017.
  • A. Doliwa. and P. Santini, An elementary geometric characterisation of the integrable motions of a curve. Physics Letters A, 185, 373-384, 1994.
  • C. Ekici, M. Dede, H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5), 1-11, 2017.
  • N. Gürbüz, Inextensible flows of spacelike, timelike and null curves. Int. J. Contemp Math Sci. 2009, 4, 1599-1604.
  • H. Hasimoto, A soliton on a vortex lament. J. Fluid Mech., 51(3), 477-485, 1959.
  • R.A. Hussien and T. Youssef, Evolution of Special Ruled Surfaces via the Evolution of Their Directrices in Euclidean 3-Space Applied Mathematics and Information Science. 10(5), 1949-1956, 2016.
  • G.U. Kaymanlı, C. Ekici and M. Dede, Directional canal surfaces in E3, Current Academic Studies in Natural Sciences and Mathematics Sciences, 63-80, 2018.
  • T. Körpınar, V. Asil and S. Baş, On characterization inextensible flows of curves according to Bishop frame, Notas de Matematica, 7(1), 37-45, 2011.
  • D.Y. Kwon, F. C. Park, Inextensible ows of curves and developable surfaces, Appl. Math. Lett., 18, 1156-1162, 2005.
  • M. Lakshmanan, T. W. Ruijgrok, C. J. Thompson, On the dynamics of a continuum spin system, Phys. A, 84(3), 577-590, 1976.
  • R. Lopez,. Differential geometry of curves and surfaces in Lorentz-Minkowski space. arXiv preprint arXiv:0810.3351, 2008.
  • B. O`Neill, Semi-Riemannian geometry with applications to relativity. Academic Press, New York, 1983.
  • M.A. Soliman, N.H. Abdel-All, R.A. Hussien and T. Youssef, Timel, Journal of Applied Mathematics and Physics. 6, 1748-1756, 2018.
  • Referans21 D. W. Yoon, Z.K. Yüzbaş and E.C. Aslan, Evolution of Spacelike Curves and Special Timelike Ruled Surfaces in the Minkowski Space, arXiv preprint arXiv:1908.00053v1, 2019.
  • Referans22 Z. K. Yüzbaşı, D. W. Yoon, Inextensible Flows of Curves on Lightlike Surfaces. Mathematics, 6(11), 224, 2018.

Timelike Uzay Eğrisi boyunca q-çatı kullanılarak doğrultmanların gelişimiyle regle yüzeylerin yönlü gelişimleri

Yıl 2020, Sayı: 20, 392 - 396, 31.12.2020
https://doi.org/10.31590/ejosat.681674

Öz

Bu çalışmada, 3 boyutlu Minkowski uzayında q-çatılı timelike uzay eğrisi boyunca normal ve binormal vektörlerle elde edilen regle yüzeyler incelendi. Doğrultmanlar kullanılarak hem quasi normal hem de quasi binormal regle yüzeylerin yönlü gelişimleri çalışıldı. Daha sonra bu regle yüzeylerin açılabilirliği, uzatılamaz olduğu ve minimal olma özellikleri gibi bazı geometrik özellikler üzerine çalıştık.

Kaynakça

  • H. N. Abd-Ellah, Evolution of translation Surfaces in Euclidean 3 space Applied Mathematics and Information Science. 9(2), 661-668, 2015.
  • K. Akutagawa and S. Nishikawa, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J. 42(2): 67-82, 1990.
  • R. Balakrishnan, R. Blumenfeld, (1997). Transformation of general curve evolution to a modified Belavin-Polyakov equation. J. Math. Phys., 38(11), 5878-5888.
  • M. Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Saddle River, 1976.
  • S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6): 305-09, 1987.
  • M. Dede, C. Ekici and A. Görgülü, Directional q-frame along a space curve, IJARCSSE. 5(12), 775-780, 2015.
  • M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra. 9(12), 527-535, 2015.
  • M. Dede, G. Tarım and C. Ekici, Timelike directional Bertrand curves in Minkowski Space, 15th International Geometry Symposium, Amasya, Turkey 2017.
  • A. Doliwa. and P. Santini, An elementary geometric characterisation of the integrable motions of a curve. Physics Letters A, 185, 373-384, 1994.
  • C. Ekici, M. Dede, H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5), 1-11, 2017.
  • N. Gürbüz, Inextensible flows of spacelike, timelike and null curves. Int. J. Contemp Math Sci. 2009, 4, 1599-1604.
  • H. Hasimoto, A soliton on a vortex lament. J. Fluid Mech., 51(3), 477-485, 1959.
  • R.A. Hussien and T. Youssef, Evolution of Special Ruled Surfaces via the Evolution of Their Directrices in Euclidean 3-Space Applied Mathematics and Information Science. 10(5), 1949-1956, 2016.
  • G.U. Kaymanlı, C. Ekici and M. Dede, Directional canal surfaces in E3, Current Academic Studies in Natural Sciences and Mathematics Sciences, 63-80, 2018.
  • T. Körpınar, V. Asil and S. Baş, On characterization inextensible flows of curves according to Bishop frame, Notas de Matematica, 7(1), 37-45, 2011.
  • D.Y. Kwon, F. C. Park, Inextensible ows of curves and developable surfaces, Appl. Math. Lett., 18, 1156-1162, 2005.
  • M. Lakshmanan, T. W. Ruijgrok, C. J. Thompson, On the dynamics of a continuum spin system, Phys. A, 84(3), 577-590, 1976.
  • R. Lopez,. Differential geometry of curves and surfaces in Lorentz-Minkowski space. arXiv preprint arXiv:0810.3351, 2008.
  • B. O`Neill, Semi-Riemannian geometry with applications to relativity. Academic Press, New York, 1983.
  • M.A. Soliman, N.H. Abdel-All, R.A. Hussien and T. Youssef, Timel, Journal of Applied Mathematics and Physics. 6, 1748-1756, 2018.
  • Referans21 D. W. Yoon, Z.K. Yüzbaş and E.C. Aslan, Evolution of Spacelike Curves and Special Timelike Ruled Surfaces in the Minkowski Space, arXiv preprint arXiv:1908.00053v1, 2019.
  • Referans22 Z. K. Yüzbaşı, D. W. Yoon, Inextensible Flows of Curves on Lightlike Surfaces. Mathematics, 6(11), 224, 2018.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Gül Ugur Kaymanli 0000-0003-4932-894X

Cumali Ekici 0000-0002-3247-5727

Mustafa Dede 0000-0003-2652-637X

Yayımlanma Tarihi 31 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Sayı: 20

Kaynak Göster

APA Ugur Kaymanli, G., Ekici, C., & Dede, M. (2020). Directional Evolution of the Ruled Surfaces via the Evolution of Their Directrix Using q-frame along a Timelike Space Curve. Avrupa Bilim Ve Teknoloji Dergisi(20), 392-396. https://doi.org/10.31590/ejosat.681674