Araştırma Makalesi
BibTex RIS Kaynak Göster

Characterizations of slant and spherical helices due to pseudo-Sabban frame

Yıl 2018, Cilt: 1 Sayı: 1, 49 - 56, 30.06.2018

Bülent Altunkaya Levent Kula

https://doi.org/10.33401/fujma.412081
Cited By: 1

Öz

In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.

Anahtar Kelimeler

Geodesic curvature Sabban frame Minkowski space Pseudosphere Hyperbolic plane Helix

Kaynakça

  • [1] Ali Ahmad, T. and Lopez, R., Slant helices in Minkowski space E3 1 , J. Korean Math. Soc. 48, no. 1, 159–167. 2011.
  • [2] Altunkaya, B. and Kula, L., Some characterizations of slant and spherical helices due to sabban frame, Mathematical Sciences and Applications E-Notes, Vol 3, No. 2, 64-73, 2015.
  • [3] Babaarslan, M. and Yaylı, Y., On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space, Annals of the Alexandru Ioan Cuza University -Mathematics, 2015. doi:10.1515/aicu-2015-0009.
  • [4] Encheva, R. and Georgiev, G., Shapes of space curves, Journal for Geometry and Graphics, Vol 7, No. 2, 145-155, 2003.
  • [5] Güner, G. and Ekmekci, N., On the spherical curves and Bertrand curves in Minkowski 3-space, J. Math. Comput. Sci., No. 4, 898-906, 2012.
  • [6] Izuyama, S., Pei, D.H., Sano, T., and Torii, E., Evolutes of hyperbolic plane curves, Acta Mathematica Sinica, Vol.20, no.3, pp. 543-550, 2004.
  • [7] Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  • [8] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space, arXiv:0810.3351v1 [math.DG], 2008.
  • [9] Pekmen, U¨ . and Pas¸alı, S., Some characterizations of Lorentzian spherical spacelike curves, Mathematica Moravica 3, 31-37, 1999.
  • [10] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical spacelike curves with the timelike and the null principal normal, Math. Moravica, 4, 83-92, 2000.
  • [11] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical timelike and null curves, Matematicki Vesnik, 53, 21-27, 2001.
  • [12] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of the spacelike, the timelike and the on the pseudohyperbolic space H2 0 in E3 1 , Krugajevac J. Math., 22, 71-82, 2000.

Yıl 2018, Cilt: 1 Sayı: 1, 49 - 56, 30.06.2018

Bülent Altunkaya Levent Kula

https://doi.org/10.33401/fujma.412081
Cited By: 1

Öz

Kaynakça

  • [1] Ali Ahmad, T. and Lopez, R., Slant helices in Minkowski space E3 1 , J. Korean Math. Soc. 48, no. 1, 159–167. 2011.
  • [2] Altunkaya, B. and Kula, L., Some characterizations of slant and spherical helices due to sabban frame, Mathematical Sciences and Applications E-Notes, Vol 3, No. 2, 64-73, 2015.
  • [3] Babaarslan, M. and Yaylı, Y., On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space, Annals of the Alexandru Ioan Cuza University -Mathematics, 2015. doi:10.1515/aicu-2015-0009.
  • [4] Encheva, R. and Georgiev, G., Shapes of space curves, Journal for Geometry and Graphics, Vol 7, No. 2, 145-155, 2003.
  • [5] Güner, G. and Ekmekci, N., On the spherical curves and Bertrand curves in Minkowski 3-space, J. Math. Comput. Sci., No. 4, 898-906, 2012.
  • [6] Izuyama, S., Pei, D.H., Sano, T., and Torii, E., Evolutes of hyperbolic plane curves, Acta Mathematica Sinica, Vol.20, no.3, pp. 543-550, 2004.
  • [7] Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  • [8] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space, arXiv:0810.3351v1 [math.DG], 2008.
  • [9] Pekmen, U¨ . and Pas¸alı, S., Some characterizations of Lorentzian spherical spacelike curves, Mathematica Moravica 3, 31-37, 1999.
  • [10] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical spacelike curves with the timelike and the null principal normal, Math. Moravica, 4, 83-92, 2000.
  • [11] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical timelike and null curves, Matematicki Vesnik, 53, 21-27, 2001.
  • [12] Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of the spacelike, the timelike and the on the pseudohyperbolic space H2 0 in E3 1 , Krugajevac J. Math., 22, 71-82, 2000.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Bülent Altunkaya

Levent Kula

Yayımlanma Tarihi 30 Haziran 2018
Gönderilme Tarihi 3 Nisan 2018
Kabul Tarihi 19 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 1

Kaynak Göster

APA Altunkaya, B., & Kula, L. (2018). Characterizations of slant and spherical helices due to pseudo-Sabban frame. Fundamental Journal of Mathematics and Applications, 1(1), 49-56. https://doi.org/10.33401/fujma.412081
AMA Altunkaya B, Kula L. Characterizations of slant and spherical helices due to pseudo-Sabban frame. FUJMA. Haziran 2018;1(1):49-56. doi:10.33401/fujma.412081
Chicago Altunkaya, Bülent, ve Levent Kula. “Characterizations of Slant and Spherical Helices Due to Pseudo-Sabban Frame”. Fundamental Journal of Mathematics and Applications 1, sy. 1 (Haziran 2018): 49-56. https://doi.org/10.33401/fujma.412081.
EndNote Altunkaya B, Kula L (01 Haziran 2018) Characterizations of slant and spherical helices due to pseudo-Sabban frame. Fundamental Journal of Mathematics and Applications 1 1 49–56.
IEEE B. Altunkaya ve L. Kula, “Characterizations of slant and spherical helices due to pseudo-Sabban frame”, FUJMA, c. 1, sy. 1, ss. 49–56, 2018, doi: 10.33401/fujma.412081.
ISNAD Altunkaya, Bülent - Kula, Levent. “Characterizations of Slant and Spherical Helices Due to Pseudo-Sabban Frame”. Fundamental Journal of Mathematics and Applications 1/1 (Haziran 2018), 49-56. https://doi.org/10.33401/fujma.412081.
JAMA Altunkaya B, Kula L. Characterizations of slant and spherical helices due to pseudo-Sabban frame. FUJMA. 2018;1:49–56.
MLA Altunkaya, Bülent ve Levent Kula. “Characterizations of Slant and Spherical Helices Due to Pseudo-Sabban Frame”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 1, 2018, ss. 49-56, doi:10.33401/fujma.412081.
Vancouver Altunkaya B, Kula L. Characterizations of slant and spherical helices due to pseudo-Sabban frame. FUJMA. 2018;1(1):49-56.

Cited By

Siacci's Theorem for Frenet Curves in Minkowski 3-Space
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.693053
 Kapak Resmi İndir

Creative Commons License
The published articles in Fundamental Journal of Mathematics and Applications are licensed under a