Citation: Ufuk Öztürk, Zeynep Büşra Alkan. Darboux helices in three dimensional Lie groups[J]. AIMS Mathematics, 2020, 5(4): 3169-3181. doi: 10.3934/math.2020204
[1] | D. J. Struik, Lectures on classical differential geometry, Reading, MA: Addison, 1988. |
[2] | S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math., 28 (2004), 153-163. |
[3] | A. Menninger, Characterization of the slant helix as successor curve of the general helix, International Electronic Journal of Geometry, 7 (2014), 84-91. doi: 10.36890/iejg.593986 |
[4] | M. Barros, A. Ferrández, P. Lucas, et al. General helices in the three-dimensional Lorentzian space forms, Rocky Mt. J. Math., 31 (2001), 373-388. doi: 10.1216/rmjm/1020171565 |
[5] | P. Lucas, J. A. Ortega-Yagües, Slant helices in the Euclidean 3-space revisited, B. Belg. Math. Soc-Sim., 23 (2016), 133-150. |
[6] | E. Ziplar, A. Senol, Y. Yayli, On Darboux helices in euclidean 3-space, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12 (2012), 73-80. |
[7] | N. Macit, M. Düldül, Relatively normal-slant helices lying on a surface and their characterizations, Hacet. J. Math. Stat., 46 (2017), 397-408. |
[8] | A. Şenol, E. Ziplar, Y. Yayli, et al. A new approach on helices in Euclidean n-space, Math. Commun., 18 (2013), 241-256. |
[9] | I. Gök, C. Camci, H. H. Hacisalihoğlu, Vn-slant helices in Euclidean n-space En, Math. Commun., 14 (2009), 317-329. |
[10] | L. Kula, N. Ekmekci, Y. Yaylı, et al. Characterizations of slant helices in Euclidean 3-space, Turk. J. Math., 34 (2010), 261-273. |
[11] | L. Kula, Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005), 600-607. |
[12] | E. Özdamar, H. H. Hacisalihoğlu, A characterization of inclined curves in Euclidean n-space, Comm. Fac. Sci. Univ. Ankara Sér. A1 Math., 24 (1975), 15-23. |
[13] | G. Öztürk, B. Bulca, B. Bayram, et al. Focal representation of k-slant helices in $\Bbb E^{m+1}$, Acta Universitatis Sapientiae, Mathematica, 7 (2015), 200-209. |
[14] | B. Uzunoğlu, I. Gök, Y. Yaylı, A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-323. |
[15] | U. Çiftçi, A generalization of Lancret's theorem, J. Geom. Phys., 59 (2009), 1597-1603. doi: 10.1016/j.geomphys.2009.07.016 |
[16] | O. Zeki Okuyucu, I. Gök, Y. Yayli, et al. Slant helices in three dimensional Lie groups, Appl. Math. Comput., 221 (2013), 672-683. |
[17] | A. Yampolsky, A. Opariy, Generalized helices in three-dimensional Lie groups, Turk. J. Math., 43 (2019), 1447-1455. doi: 10.3906/mat-1806-33 |
[18] | N. do Espírito-Santo, S. Fornari, K. Frensel, et al. Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric, Manuscripta Math., 111 (2003), 459-470. doi: 10.1007/s00229-003-0357-5 |