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

Year 2018, Volume: 1 Issue: 1, 49 - 56, 30.06.2018

Bülent Altunkaya Levent Kula

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

Abstract

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.

Keywords

Geodesic curvature Sabban frame Minkowski space Pseudosphere Hyperbolic plane Helix

References

  • [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.

Year 2018, Volume: 1 Issue: 1, 49 - 56, 30.06.2018

Bülent Altunkaya Levent Kula

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

Abstract

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Bülent Altunkaya

Levent Kula

Publication Date June 30, 2018
Submission Date April 3, 2018
Acceptance Date April 19, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

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. June 2018;1(1):49-56. doi:10.33401/fujma.412081
Chicago Altunkaya, Bülent, and Levent Kula. “Characterizations of Slant and Spherical Helices Due to Pseudo-Sabban Frame”. Fundamental Journal of Mathematics and Applications 1, no. 1 (June 2018): 49-56. https://doi.org/10.33401/fujma.412081.
EndNote Altunkaya B, Kula L (June 1, 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 and L. Kula, “Characterizations of slant and spherical helices due to pseudo-Sabban frame”, FUJMA, vol. 1, no. 1, pp. 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 (June 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 and Levent Kula. “Characterizations of Slant and Spherical Helices Due to Pseudo-Sabban Frame”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 1, 2018, pp. 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.

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