Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2025, Cilt: 13 Sayı: 1, 8 - 17, 27.06.2025

Süleyman Şenyurt , Davut Canlı , Kebire Hilal Ayvacı Şimşek

https://doi.org/10.51354/mjen.1440372

Öz

Proje Numarası

None

Kaynakça

  • [1] P. Do-Carmo, “Differential geometry of curves and surfaces: revised and updated second edition”, Courier Dover Publications, 2016.
  • [2] E. Abbena, S. Salamon and A. Gray, “Modern differential geometry of curves and surfaces with Mathematica”, Chapman and Hall/CRC, 2017.
  • [3] H. H. Hacısaliho˘glu , “Differential geometry II”, AnkaraUniversity Press, 2000.
  • [4] D. J. Struik, “Lectures on classical differential geometry”, Courier Corporation, 2012.
  • [5] M. Juza, “Ligne de striction sur unegeneralisation a plusierurs dimensions d’une surface regle”, Czechoslovak Mathematical Journal 12(87) (1962), 243-250.
  • [6] S. Ouarab and A. O. Chahdi, “Some characteristic properties of ruled surface with Frenet frame of an arbitrary non-cylindrical ruled surface in Euclidean 3-space”, International Journal of Applied Physics and Mathematics 10(1) (2020), 16-24.
  • [7] R. L. Bishop, “There is more than one way to frame a curve”, The American Mathematical Monthly 82 (1975), 246-251.
  • [8] M. Masal and A. Z. Azak, “Ruled surfaces according to Bishop frame in the Euclidean 3-space”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 89(2) (2019), 415-424.
  • [9] Y. Tunc¸er, “Ruled surfaces with the Bishop frame in Euclidean 3–space”, Gen. Math. Notes 26 (2015), 74-83.
  • [10] S. Ouarab, A. O. Chahdi, M. Izid, “Ruled surfaces with alternative moving frame in Euclidean 3-space”, International Journal of Mathematical Sciences and Engineering Applications 12(2) (2018), 43-58.
  • [11] S. S¸enyurt and K. Eren, “On ruled surfaces with Sannia frame in Euclidean 3-space”, Kyungpook Mathematical Journal 62 (2022), 509-531.
  • [12] S. S¸enyurt and K. Eren, “On ruled surfaces with Sannia frame in Euclidean 3-space”, Kyungpook Mathematical Journal 62 (2022), 509-531. A. Elsharkawy, H. Elsayied, and A. Refaat, “Quasi Ruled Surfaces in Euclidean 3-space”, European Journal of Pure and Applied Mathematics, 18(1), 5710-5710.
  • [13] S. Ouarab, “Corrigendum to Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in 𝐸3”, Abstract and Applied Analysis 2022 (2022).
  • [14] M. Turgut and S. Yılmaz, “Smarandache Curves in Minkowski Spacetime”, International Journal of Mathematical Combinatorics 3 (2008), 51-55.
  • [15] A.T. Ali, “Special Smarandache curves in the Euclidean space”, International Journal of Mathematical Combinatorics 2 (2010), 30-36.
  • [16] S. Ouarab, “Smarandache Ruled Surfaces according to Darboux Frame in 𝐸3”, Journal of Mathematics 2021 (2021).
  • [17] S. Ouarab, “NC-Smarandache Ruled Surface and NWSmarandache Ruled Surface according to Alternative Moving Frame in 𝐸3”, Journal of Mathematics 2021 (2021).
  • [18] S. S¸enyurt, D. Canlı and C¸ . Elif, “Smarandache-Based Ruled Surfaces with the Darboux Vector According to Frenet Frame in 𝐸3”, Journal of New Theory, 39, (2022), 8-18.
  • [19] S. S¸enyurt, D. Canlı and C¸ . Elif, “Some special Smarandache ruled surfaces by Frenet Frame in 𝐸3 - I”, Turkish Journal of Science, 7, (2022), 31-42.
  • [20] S. S¸enyurt, D. Canlı, C¸ . Elif and S. G. Mazlum, “Some special Smarandache ruled surfaces by Frenet frame in 𝐸3 -II”, Honam Mathematical Journal, 44(4), (2022), 594-617.
  • [21] B. B¨ukc¨u, M. K. Karacan, “The slant helices according to Bishop frame”, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences, 3 (2009), 67-70.

Ruled Surfaces with Bishop vectors via Smarandache geometry

Yıl 2025, Cilt: 13 Sayı: 1, 8 - 17, 27.06.2025

Süleyman Şenyurt , Davut Canlı , Kebire Hilal Ayvacı Şimşek

https://doi.org/10.51354/mjen.1440372

Öz

The paper studies new ruled surfaces with the vectors of Bishop frame via Smarandache geometry. The fundamental forms and the corresponding curvatures are provided for each ruled surface to draw characteristics of the surfaces such as developability and minimality. Moreover, the properties of the base curve and the corresponding striction curves of each surface are also discussed through asymptoticity, geodesicity and principal line. It is found that a ruled surface designed by Bishop vectors of a slant helix-like curve apart from other special kinds of curves has a direct effect on the characteristics of some constructed ruled surfaces.

Anahtar Kelimeler

Bishop frame Smarandache ruled surfaces fundamental forms mean and Gaussian curvatures developable and minimal surfaces

Etik Beyan

No need

Destekleyen Kurum

None

Proje Numarası

None

Teşekkür

We would like to thank the editors of the journal for taking care of the manuscript.

Kaynakça

  • [1] P. Do-Carmo, “Differential geometry of curves and surfaces: revised and updated second edition”, Courier Dover Publications, 2016.
  • [2] E. Abbena, S. Salamon and A. Gray, “Modern differential geometry of curves and surfaces with Mathematica”, Chapman and Hall/CRC, 2017.
  • [3] H. H. Hacısaliho˘glu , “Differential geometry II”, AnkaraUniversity Press, 2000.
  • [4] D. J. Struik, “Lectures on classical differential geometry”, Courier Corporation, 2012.
  • [5] M. Juza, “Ligne de striction sur unegeneralisation a plusierurs dimensions d’une surface regle”, Czechoslovak Mathematical Journal 12(87) (1962), 243-250.
  • [6] S. Ouarab and A. O. Chahdi, “Some characteristic properties of ruled surface with Frenet frame of an arbitrary non-cylindrical ruled surface in Euclidean 3-space”, International Journal of Applied Physics and Mathematics 10(1) (2020), 16-24.
  • [7] R. L. Bishop, “There is more than one way to frame a curve”, The American Mathematical Monthly 82 (1975), 246-251.
  • [8] M. Masal and A. Z. Azak, “Ruled surfaces according to Bishop frame in the Euclidean 3-space”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 89(2) (2019), 415-424.
  • [9] Y. Tunc¸er, “Ruled surfaces with the Bishop frame in Euclidean 3–space”, Gen. Math. Notes 26 (2015), 74-83.
  • [10] S. Ouarab, A. O. Chahdi, M. Izid, “Ruled surfaces with alternative moving frame in Euclidean 3-space”, International Journal of Mathematical Sciences and Engineering Applications 12(2) (2018), 43-58.
  • [11] S. S¸enyurt and K. Eren, “On ruled surfaces with Sannia frame in Euclidean 3-space”, Kyungpook Mathematical Journal 62 (2022), 509-531.
  • [12] S. S¸enyurt and K. Eren, “On ruled surfaces with Sannia frame in Euclidean 3-space”, Kyungpook Mathematical Journal 62 (2022), 509-531. A. Elsharkawy, H. Elsayied, and A. Refaat, “Quasi Ruled Surfaces in Euclidean 3-space”, European Journal of Pure and Applied Mathematics, 18(1), 5710-5710.
  • [13] S. Ouarab, “Corrigendum to Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in 𝐸3”, Abstract and Applied Analysis 2022 (2022).
  • [14] M. Turgut and S. Yılmaz, “Smarandache Curves in Minkowski Spacetime”, International Journal of Mathematical Combinatorics 3 (2008), 51-55.
  • [15] A.T. Ali, “Special Smarandache curves in the Euclidean space”, International Journal of Mathematical Combinatorics 2 (2010), 30-36.
  • [16] S. Ouarab, “Smarandache Ruled Surfaces according to Darboux Frame in 𝐸3”, Journal of Mathematics 2021 (2021).
  • [17] S. Ouarab, “NC-Smarandache Ruled Surface and NWSmarandache Ruled Surface according to Alternative Moving Frame in 𝐸3”, Journal of Mathematics 2021 (2021).
  • [18] S. S¸enyurt, D. Canlı and C¸ . Elif, “Smarandache-Based Ruled Surfaces with the Darboux Vector According to Frenet Frame in 𝐸3”, Journal of New Theory, 39, (2022), 8-18.
  • [19] S. S¸enyurt, D. Canlı and C¸ . Elif, “Some special Smarandache ruled surfaces by Frenet Frame in 𝐸3 - I”, Turkish Journal of Science, 7, (2022), 31-42.
  • [20] S. S¸enyurt, D. Canlı, C¸ . Elif and S. G. Mazlum, “Some special Smarandache ruled surfaces by Frenet frame in 𝐸3 -II”, Honam Mathematical Journal, 44(4), (2022), 594-617.
  • [21] B. B¨ukc¨u, M. K. Karacan, “The slant helices according to Bishop frame”, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences, 3 (2009), 67-70.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Araştırma Makalesi
Yazarlar

Süleyman Şenyurt 0000-0003-1097-5541

Davut Canlı 0000-0003-0405-9969

Kebire Hilal Ayvacı Şimşek 0000-0002-5114-5475

Proje Numarası None
Yayımlanma Tarihi 27 Haziran 2025
Gönderilme Tarihi 20 Şubat 2024
Kabul Tarihi 17 Haziran 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 13 Sayı: 1

Kaynak Göster

APA Şenyurt, S., Canlı, D., & Ayvacı Şimşek, K. H. (2025). Ruled Surfaces with Bishop vectors via Smarandache geometry. MANAS Journal of Engineering, 13(1), 8-17. https://doi.org/10.51354/mjen.1440372
AMA Şenyurt S, Canlı D, Ayvacı Şimşek KH. Ruled Surfaces with Bishop vectors via Smarandache geometry. MJEN. Haziran 2025;13(1):8-17. doi:10.51354/mjen.1440372
Chicago Şenyurt, Süleyman, Davut Canlı, ve Kebire Hilal Ayvacı Şimşek. “Ruled Surfaces With Bishop Vectors via Smarandache Geometry”. MANAS Journal of Engineering 13, sy. 1 (Haziran 2025): 8-17. https://doi.org/10.51354/mjen.1440372.
EndNote Şenyurt S, Canlı D, Ayvacı Şimşek KH (01 Haziran 2025) Ruled Surfaces with Bishop vectors via Smarandache geometry. MANAS Journal of Engineering 13 1 8–17.
IEEE S. Şenyurt, D. Canlı, ve K. H. Ayvacı Şimşek, “Ruled Surfaces with Bishop vectors via Smarandache geometry”, MJEN, c. 13, sy. 1, ss. 8–17, 2025, doi: 10.51354/mjen.1440372.
ISNAD Şenyurt, Süleyman vd. “Ruled Surfaces With Bishop Vectors via Smarandache Geometry”. MANAS Journal of Engineering 13/1 (Haziran 2025), 8-17. https://doi.org/10.51354/mjen.1440372.
JAMA Şenyurt S, Canlı D, Ayvacı Şimşek KH. Ruled Surfaces with Bishop vectors via Smarandache geometry. MJEN. 2025;13:8–17.
MLA Şenyurt, Süleyman vd. “Ruled Surfaces With Bishop Vectors via Smarandache Geometry”. MANAS Journal of Engineering, c. 13, sy. 1, 2025, ss. 8-17, doi:10.51354/mjen.1440372.
Vancouver Şenyurt S, Canlı D, Ayvacı Şimşek KH. Ruled Surfaces with Bishop vectors via Smarandache geometry. MJEN. 2025;13(1):8-17.
 Kapak Resmi İndir

Manas Journal of Engineering 

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