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Year 2019, Volume: 68 Issue: 1, 1175 - 1185, 01.02.2019

O. Zeki Okuyucu Caner Değirmen Ö. Gökmen Yıldız

https://doi.org/10.31801/cfsuasmas.511677
Cited By: 2

Abstract

References

  • Ahmad, T. Ali, Special Smarandache Curves in the Euclidean Space, International J.Math. Combin., (2010), 2, 30-36.
  • Bektaş, Ö. and Yüce, S., Special Smarandache Curves According to Darboux Frame in E³, Romanian J. of Math and Comp. Sci., (2013), 3(1), 48-59.
  • Bozkurt, Z., Gök, İ., Okuyucu, O. Z. and Ekmekci, F. N., Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups, Life Science Journal, (2013), 10(3), 819-823.
  • Crouch, P. and Silva Leite, F., The dynamic interpolation problem:on Riemannian manifoldsi Lie groups and symmetric spaces, J. Dyn. Control Syst., (1995), 1(2), 177-202.
  • Çiftçi, Ü., A generalization of Lancert's theorem, J. Geom. Phys., (2009), 59, 1597-1603.
  • Çöken, A. C., and Çiftci Ü., A note on the geometry of Lie groups, Nonlinear Anal. TMA, (2008), 68, 2013-2016.
  • Gök, İ., Okuyucu, O. Z., Ekmekci, N. and Yaylı, Y., On Mannheim Partner Curves in three Dimensional Lie Groups, Miskolc Mathematical Notes, (2014), 15(2), 467-479.
  • Gürses, B. N., Bektaş, Ö. and Yüce, S., Special Smarandache Curves in R³₁, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., (2016), 65(2), 143-160.
  • Taşköprü, K. and Tosun, M., Smarandache Curves on S² ,Boletim da Sociedade Paranaense de Matemática 3 srie., (2014), 32(1), 51-59.
  • Turgut, M. and Yılmaz, S., Smarandache Curves in Minkowski Space-time, International J. Math. Combin., (2008), 3, 51-55.
  • Okuyucu, O. Z., Gök, İ., Yaylı, Y. and Ekmekci, N., Slant Helices in three Dimensional Lie Groups, Appl. Math.Comput., (2013), 221, 672-683.
  • Okuyucu, O. Z., Gök, İ., Yaylı, Y. and Ekmekci, N., Bertrand Curves in three Dimensional Lie Groups, Miskolc Mathematical Notes, (2017), 17(2), 999-1010.
  • Okuyucu, Z., Yıldız, Ö. G. and Tosun, M., Spinor Frenet Equations in Three Dimensional Lie Groups, Adv. Appl. Clifford Algebras, (2016), 26(4), 1341-1348.
  • Körpınar, T., A New Version of Energy for Slant Helix with Bending Energy in the Lie Groups, Journal of Science and Arts, (2017), 4(41), 721-730.
  • Körpınar, T., A New Version of the Energy of Tangent Indicatrix with Dynamics System in Lie Group, Differ. Equ. Dyn. Syst., (2018), https://doi.org/10.1007/s12591-018-0413-y.

Smarandache Curves in three dimensional Lie groups

Year 2019, Volume: 68 Issue: 1, 1175 - 1185, 01.02.2019

O. Zeki Okuyucu Caner Değirmen Ö. Gökmen Yıldız

https://doi.org/10.31801/cfsuasmas.511677
Cited By: 2

Abstract

In this paper, we introduce special Smarandache curves and obtain Frenet apparatus of a Smarandache curve in three dimensional Lie groups with a bi-invariant metric. Moreover, we give some relations between a helix or a slant helix curve and its Smarandache curve in three dimensional Lie groups.

Keywords

Smarandache curves Lie groups helices.

References

  • Ahmad, T. Ali, Special Smarandache Curves in the Euclidean Space, International J.Math. Combin., (2010), 2, 30-36.
  • Bektaş, Ö. and Yüce, S., Special Smarandache Curves According to Darboux Frame in E³, Romanian J. of Math and Comp. Sci., (2013), 3(1), 48-59.
  • Bozkurt, Z., Gök, İ., Okuyucu, O. Z. and Ekmekci, F. N., Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups, Life Science Journal, (2013), 10(3), 819-823.
  • Crouch, P. and Silva Leite, F., The dynamic interpolation problem:on Riemannian manifoldsi Lie groups and symmetric spaces, J. Dyn. Control Syst., (1995), 1(2), 177-202.
  • Çiftçi, Ü., A generalization of Lancert's theorem, J. Geom. Phys., (2009), 59, 1597-1603.
  • Çöken, A. C., and Çiftci Ü., A note on the geometry of Lie groups, Nonlinear Anal. TMA, (2008), 68, 2013-2016.
  • Gök, İ., Okuyucu, O. Z., Ekmekci, N. and Yaylı, Y., On Mannheim Partner Curves in three Dimensional Lie Groups, Miskolc Mathematical Notes, (2014), 15(2), 467-479.
  • Gürses, B. N., Bektaş, Ö. and Yüce, S., Special Smarandache Curves in R³₁, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., (2016), 65(2), 143-160.
  • Taşköprü, K. and Tosun, M., Smarandache Curves on S² ,Boletim da Sociedade Paranaense de Matemática 3 srie., (2014), 32(1), 51-59.
  • Turgut, M. and Yılmaz, S., Smarandache Curves in Minkowski Space-time, International J. Math. Combin., (2008), 3, 51-55.
  • Okuyucu, O. Z., Gök, İ., Yaylı, Y. and Ekmekci, N., Slant Helices in three Dimensional Lie Groups, Appl. Math.Comput., (2013), 221, 672-683.
  • Okuyucu, O. Z., Gök, İ., Yaylı, Y. and Ekmekci, N., Bertrand Curves in three Dimensional Lie Groups, Miskolc Mathematical Notes, (2017), 17(2), 999-1010.
  • Okuyucu, Z., Yıldız, Ö. G. and Tosun, M., Spinor Frenet Equations in Three Dimensional Lie Groups, Adv. Appl. Clifford Algebras, (2016), 26(4), 1341-1348.
  • Körpınar, T., A New Version of Energy for Slant Helix with Bending Energy in the Lie Groups, Journal of Science and Arts, (2017), 4(41), 721-730.
  • Körpınar, T., A New Version of the Energy of Tangent Indicatrix with Dynamics System in Lie Group, Differ. Equ. Dyn. Syst., (2018), https://doi.org/10.1007/s12591-018-0413-y.
There are 15 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

O. Zeki Okuyucu 0000-0003-4379-0252

Caner Değirmen This is me

Ö. Gökmen Yıldız 0000-0002-2760-1223

Publication Date February 1, 2019
Submission Date May 25, 2018
Acceptance Date September 28, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Okuyucu, O. Z., Değirmen, C., & Yıldız, Ö. G. (2019). Smarandache Curves in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1175-1185. https://doi.org/10.31801/cfsuasmas.511677
AMA Okuyucu OZ, Değirmen C, Yıldız ÖG. Smarandache Curves in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):1175-1185. doi:10.31801/cfsuasmas.511677
Chicago Okuyucu, O. Zeki, Caner Değirmen, and Ö. Gökmen Yıldız. “Smarandache Curves in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 1175-85. https://doi.org/10.31801/cfsuasmas.511677.
EndNote Okuyucu OZ, Değirmen C, Yıldız ÖG (February 1, 2019) Smarandache Curves in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1175–1185.
IEEE O. Z. Okuyucu, C. Değirmen, and Ö. G. Yıldız, “Smarandache Curves in three dimensional Lie groups”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 1175–1185, 2019, doi: 10.31801/cfsuasmas.511677.
ISNAD Okuyucu, O. Zeki et al. “Smarandache Curves in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 1175-1185. https://doi.org/10.31801/cfsuasmas.511677.
JAMA Okuyucu OZ, Değirmen C, Yıldız ÖG. Smarandache Curves in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1175–1185.
MLA Okuyucu, O. Zeki et al. “Smarandache Curves in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 1175-8, doi:10.31801/cfsuasmas.511677.
Vancouver Okuyucu OZ, Değirmen C, Yıldız ÖG. Smarandache Curves in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1175-8.

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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