TY - JOUR T1 - Smarandache Curves in three dimensional Lie groups AU - Okuyucu, O. Zeki AU - Değirmen, Caner AU - Yıldız, Ö. Gökmen PY - 2019 DA - February Y2 - 2018 DO - 10.31801/cfsuasmas.511677 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 1175 EP - 1185 VL - 68 IS - 1 LA - en AB - 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. KW - Smarandache curves KW - Lie groups KW - helices. CR - Ahmad, T. Ali, Special Smarandache Curves in the Euclidean Space, International J.Math. Combin., (2010), 2, 30-36. CR - 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. CR - 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. CR - 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. CR - Çiftçi, Ü., A generalization of Lancert's theorem, J. Geom. Phys., (2009), 59, 1597-1603. CR - Çöken, A. C., and Çiftci Ü., A note on the geometry of Lie groups, Nonlinear Anal. TMA, (2008), 68, 2013-2016. CR - 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. CR - 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. CR - Taşköprü, K. and Tosun, M., Smarandache Curves on S² ,Boletim da Sociedade Paranaense de Matemática 3 srie., (2014), 32(1), 51-59. CR - Turgut, M. and Yılmaz, S., Smarandache Curves in Minkowski Space-time, International J. Math. Combin., (2008), 3, 51-55. CR - Okuyucu, O. Z., Gök, İ., Yaylı, Y. and Ekmekci, N., Slant Helices in three Dimensional Lie Groups, Appl. Math.Comput., (2013), 221, 672-683. CR - 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. CR - 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. CR - 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. CR - 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. UR - https://doi.org/10.31801/cfsuasmas.511677 L1 - https://dergipark.org.tr/en/download/article-file/624351 ER -