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Characterizations of Adjoint Curves According to Alternative Moving Frame

Yıl 2022, Cilt: 5 Sayı: 1, 42 - 50, 01.03.2022

Ali Çakmak Volkan Şahin

https://doi.org/10.33401/fujma.1001730
Cited By: 4

Öz

In this paper, the adjoint curve is defined by using the alternative moving frame of a unit speed space curve in 3-dimensional Euclidean space. The relationships between Frenet vectors and alternative moving frame vectors of the curve are used to offer various characterizations. Besides, ruled surfaces are constructed with the curve and its adjoint curve, and their properties are examined. In the last section, there are examples of the curves and surfaces defined in the previous sections.

Anahtar Kelimeler

Adjoint curve Alternative moving frame Distribution parameter Ruled surface

Kaynakça

  • [1] A. T. Ali, Position vectors of slant helices in Euclidean space E3, J. Egypt Math. Soc., 20 (2012), 1-6.
  • [2] L. Kula, Y. Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005), 600-607.
  • [3] M. Babaarslan, Y. A. Tando˘gan, Y. Yaylı, A note on Bertrand curves and constant slope surfaces according to Darboux frame, J. Adv. Math. Stud., 5 (2012), 87-96.
  • [4] A. T. Ali, New special curves and their spherical indicatrices, Glob. J. Adv. Res. Class. Mod. Geom., 1 (2012), 28-38.
  • [5] J. H. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput., 218 (2012), 9116-9124.
  • [6] S. K. Nurkan, ˙I. A. Güven, M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space, Prc. Natl. Acad. Sci. India Sect. A Phys. Sci., 89(1) (2019), 155-161.
  • [7] N. Macit, M. Düldül, Some new associated curves of a Frenet curve in E3 and E4, Turk J. Math., 38 (2014), 1023-1037.
  • [8] B. Uzunoğlu, I. Gök, Y. Yaylı, A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-323.
  • [9] L. Buse, M. Elkadi, A. Galligo, A computational study of ruled surfaces, J. Symb. Comput., 44(3) (2009), 232-241.
  • [10] E. Damar, N. Yüksel, A. T. Vanlı, The ruled surfaces according to type-2 Bishop frame in E3, Int. Math. Forum, 12(3) (2017), 133-143.
  • [11] F. Güler, The timelike ruled surfaces according to type-2 Bishop frame in Minkowski 3-space, J. Sci. Arts, 18 (243) (2018), 323-330.
  • [12] Ş. Kılıçoğlu, H. H. Hacısaliho˘glu, On the ruled surfaces whose frame is the Bishop frame in the Euclidean 3-space, Int. Electron. J. Geom., 6(2) (2013), 110-117.
  • [13] Y. Liu, H. Pottmann, J. Wallner, Y. Yang, W. Wang, Geometric modeling with conical meshes and developable surfaces, ACM Trans. Graph., 25(3) (2006), 681-689.
  • [14] Y. Yu, H. Liu, S. D. Jung, Structure and characterization of ruled surfaces in Euclidean 3-space, Appl. Math. Comp., 233 (2014),252-259.
  • [15] B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966.
  • [16] D. J. Struik, Lectures on Classical Differential Geometry, Dover Publication. Newyork, 1988.
  • [17] B. Şahiner, Ruled surfaces according to alternative moving frame, (2019), arXiv:1910.06589 [math.DG].
  • [18] S. Ouarab, A. O. Chahdi, M. Izid, Ruled surfaces with alternative moving frame in Euclidean 3-space, Int. J. Math. Sci. Eng. Appl., 12(2) (2018), 43-58.

Yıl 2022, Cilt: 5 Sayı: 1, 42 - 50, 01.03.2022

Ali Çakmak Volkan Şahin

https://doi.org/10.33401/fujma.1001730
Cited By: 4

Öz

Kaynakça

  • [1] A. T. Ali, Position vectors of slant helices in Euclidean space E3, J. Egypt Math. Soc., 20 (2012), 1-6.
  • [2] L. Kula, Y. Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005), 600-607.
  • [3] M. Babaarslan, Y. A. Tando˘gan, Y. Yaylı, A note on Bertrand curves and constant slope surfaces according to Darboux frame, J. Adv. Math. Stud., 5 (2012), 87-96.
  • [4] A. T. Ali, New special curves and their spherical indicatrices, Glob. J. Adv. Res. Class. Mod. Geom., 1 (2012), 28-38.
  • [5] J. H. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput., 218 (2012), 9116-9124.
  • [6] S. K. Nurkan, ˙I. A. Güven, M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space, Prc. Natl. Acad. Sci. India Sect. A Phys. Sci., 89(1) (2019), 155-161.
  • [7] N. Macit, M. Düldül, Some new associated curves of a Frenet curve in E3 and E4, Turk J. Math., 38 (2014), 1023-1037.
  • [8] B. Uzunoğlu, I. Gök, Y. Yaylı, A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-323.
  • [9] L. Buse, M. Elkadi, A. Galligo, A computational study of ruled surfaces, J. Symb. Comput., 44(3) (2009), 232-241.
  • [10] E. Damar, N. Yüksel, A. T. Vanlı, The ruled surfaces according to type-2 Bishop frame in E3, Int. Math. Forum, 12(3) (2017), 133-143.
  • [11] F. Güler, The timelike ruled surfaces according to type-2 Bishop frame in Minkowski 3-space, J. Sci. Arts, 18 (243) (2018), 323-330.
  • [12] Ş. Kılıçoğlu, H. H. Hacısaliho˘glu, On the ruled surfaces whose frame is the Bishop frame in the Euclidean 3-space, Int. Electron. J. Geom., 6(2) (2013), 110-117.
  • [13] Y. Liu, H. Pottmann, J. Wallner, Y. Yang, W. Wang, Geometric modeling with conical meshes and developable surfaces, ACM Trans. Graph., 25(3) (2006), 681-689.
  • [14] Y. Yu, H. Liu, S. D. Jung, Structure and characterization of ruled surfaces in Euclidean 3-space, Appl. Math. Comp., 233 (2014),252-259.
  • [15] B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966.
  • [16] D. J. Struik, Lectures on Classical Differential Geometry, Dover Publication. Newyork, 1988.
  • [17] B. Şahiner, Ruled surfaces according to alternative moving frame, (2019), arXiv:1910.06589 [math.DG].
  • [18] S. Ouarab, A. O. Chahdi, M. Izid, Ruled surfaces with alternative moving frame in Euclidean 3-space, Int. J. Math. Sci. Eng. Appl., 12(2) (2018), 43-58.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ali Çakmak 0000-0002-2783-9311

Volkan Şahin 0000-0001-6248-1346

Erken Görünüm Tarihi 13 Şubat 2022
Yayımlanma Tarihi 1 Mart 2022
Gönderilme Tarihi 27 Eylül 2021
Kabul Tarihi 12 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 1

Kaynak Göster

APA Çakmak, A., & Şahin, V. (2022). Characterizations of Adjoint Curves According to Alternative Moving Frame. Fundamental Journal of Mathematics and Applications, 5(1), 42-50. https://doi.org/10.33401/fujma.1001730
AMA Çakmak A, Şahin V. Characterizations of Adjoint Curves According to Alternative Moving Frame. FUJMA. Mart 2022;5(1):42-50. doi:10.33401/fujma.1001730
Chicago Çakmak, Ali, ve Volkan Şahin. “Characterizations of Adjoint Curves According to Alternative Moving Frame”. Fundamental Journal of Mathematics and Applications 5, sy. 1 (Mart 2022): 42-50. https://doi.org/10.33401/fujma.1001730.
EndNote Çakmak A, Şahin V (01 Mart 2022) Characterizations of Adjoint Curves According to Alternative Moving Frame. Fundamental Journal of Mathematics and Applications 5 1 42–50.
IEEE A. Çakmak ve V. Şahin, “Characterizations of Adjoint Curves According to Alternative Moving Frame”, FUJMA, c. 5, sy. 1, ss. 42–50, 2022, doi: 10.33401/fujma.1001730.
ISNAD Çakmak, Ali - Şahin, Volkan. “Characterizations of Adjoint Curves According to Alternative Moving Frame”. Fundamental Journal of Mathematics and Applications 5/1 (Mart 2022), 42-50. https://doi.org/10.33401/fujma.1001730.
JAMA Çakmak A, Şahin V. Characterizations of Adjoint Curves According to Alternative Moving Frame. FUJMA. 2022;5:42–50.
MLA Çakmak, Ali ve Volkan Şahin. “Characterizations of Adjoint Curves According to Alternative Moving Frame”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 1, 2022, ss. 42-50, doi:10.33401/fujma.1001730.
Vancouver Çakmak A, Şahin V. Characterizations of Adjoint Curves According to Alternative Moving Frame. FUJMA. 2022;5(1):42-50.

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Turkish Journal of Mathematics and Computer Science
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