Yıl 2019, Cilt 68, Sayı 1, Sayfalar 1175 - 1185 2018-04-11

Smarandache Curves in three dimensional Lie groups

O. Zeki Okuyucu [1] , Caner Değirmen [2] , Ö. Gökmen Yıldız [3]

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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.
Smarandache curves, Lie groups, helices.
  • 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.
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Orcid: 0000-0003-4379-0252
Yazar: O. Zeki Okuyucu

Yazar: Caner Değirmen

Orcid: 0000-0002-2760-1223
Yazar: Ö. Gökmen Yıldız

Bibtex @araştırma makalesi { cfsuasmas511677, journal = {Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, issn = {1303-5991}, eissn = {2618-6470}, address = {Ankara Üniversitesi}, year = {2018}, volume = {68}, pages = {1175 - 1185}, doi = {10.31801/cfsuasmas.511677}, title = {Smarandache Curves in three dimensional Lie groups}, key = {cite}, author = {Yıldız, Ö. Gökmen and Okuyucu, O. Zeki and Değirmen, Caner} }
APA Okuyucu, O , Değirmen, C , Yıldız, Ö . (2018). Smarandache Curves in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (1), 1175-1185. Retrieved from http://dergipark.gov.tr/cfsuasmas/issue/36517/511677
MLA Okuyucu, O , Değirmen, C , Yıldız, Ö . "Smarandache Curves in three dimensional Lie groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2018): 1175-1185 <http://dergipark.gov.tr/cfsuasmas/issue/36517/511677>
Chicago Okuyucu, O , Değirmen, C , Yıldız, Ö . "Smarandache Curves in three dimensional Lie groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2018): 1175-1185
RIS TY - JOUR T1 - Smarandache Curves in three dimensional Lie groups AU - O. Zeki Okuyucu , Caner Değirmen , Ö. Gökmen Yıldız Y1 - 2018 PY - 2018 N1 - DO - T2 - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JF - Journal JO - JOR SP - 1175 EP - 1185 VL - 68 IS - 1 SN - 1303-5991-2618-6470 M3 - UR - Y2 - 2018 ER -
EndNote %0 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Smarandache Curves in three dimensional Lie groups %A O. Zeki Okuyucu , Caner Değirmen , Ö. Gökmen Yıldız %T Smarandache Curves in three dimensional Lie groups %D 2018 %J Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics %P 1303-5991-2618-6470 %V 68 %N 1 %R %U
ISNAD Okuyucu, O. Zeki , Değirmen, Caner , Yıldız, Ö. Gökmen . "Smarandache Curves in three dimensional Lie groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 / 1 (Nisan 2018): 1175-1185.