Darboux curves in three dimensional Heisenberg group
Résumé
In this paper, a new characterization for Darboux curves in Heis₃ is completely given. Then, a new classification for translation surface , which is generated by Darboux curve in Heis₃ is obtained.
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Références
M. C¸etin, Y. Tuncer and N. Ekmekci, Translation surfaces in Euclidean 3- Space, International Journal of Information and Mathematical Sciences, 6(4) (2010), 227-231.
A. A. Ergin, On the generalized Darboux curves, Commun. Fac. Sci. Univ. Ank. Series A1, 41 (1992), 73-77.
A. A. Ergin, Timelike Darboux curves on a timelike surface M M3 1, Hadronic Journal, 24 (2001), 701-712.
R. Garcia, R. Langevin, P. Walczak, Darboux curves on surfaces, 69 (2017), 1- 24.
T. Ikawa, On curves and submanifolds in an indefinite-Riemannian manifold, Tsukuba J. Math., 9 (2) (1985), 353-371.
J. Inoguchi, R. Lopez, and M. Munteanu, Minimal translation surfaces in the Heisenberg group Nil3, Geom Dedicata, 161 (2012), 221-231.
T. Korpınar, E. Turhan, On characterization of timelike biharmonic D-helices according to Darboux frame on non-degenerate timelike surfaces in the Lorentzian Heisenberg group H, Annals of Fuzzy Mathematics and Informatics, 4 (2012), 393-400.
T. Korpınar, B-tubular surfaces in Lorentzian Heisenberg Group H3, Acta Scientiarum. Technology 37(1) (2015), 63–69
T. Korpınar, New Characterization for Minimizing Energy of Biharmonic Particles in Heisenberg Spacetime, Int J Phys.53 (2014), 3208-3218
T. Korpınar, New characterization of b-m2 developable surfaces, Acta Scientiarum. Technology 37(2) (2015), 245–250
T. Korpınar, On the Fermi–Walker Derivative for Inextensible Flows, Zeitschrift f¨ur Naturforschung A. 70 (7) (2015), 477–482
T. Korpınar, E. Turhan: A New Version of Inextensible Flows of Spacelike Curves with Timelike B2 in Minkowski Space-Time E4 1, Differ. Equ. Dyn. Syst., 21 (3) (2013), 281–290.
Lopez, R., Munteanu, M, Minimal translation surfaces in Sol3, J. Math. Soc. Japan, 64 (2012), 985-1003.
M. Munteanu, A. I. Nistor, New results on the geometry of translation surfaces, Tenth International Conference on Geometry, Integrability and Quantization, (2009), 1-12.
M. Munteanu, A. I. Nistor, On the geometry of the second fundamental form of translation surfaces in E3, arXiv:0812.3166v1 [math.DG] (2008).
M. Ozdemir, A. A. Ergin, Spacelike Darboux curves in Minkowski n-space, Differential Geometry - Dynamical Systems, 9 (2007), 131-137.
G. Saban, Sopra una carattarizza zino della sfera, Rendiconti Atti Della Accademia Nazionale Dei Lincei. CCCL VII A., (1960), 345-349.
L. Verstraelen, J. Walrave, and S. Yaprak, The minimal translation surfaces in Euclidean space, Soochow Journal of Mathematics, 20(1994), 77- 82.
Yoon, D. W., On the Gauss map of translation surfaces in Minkowski 3- space, Taiwanese Journal of Mathematics, 6 (2002), 389-398.
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