×

Special Bertrand curves in 4D Galilean space. (English) Zbl 1407.53004

Summary: The generalization of Bertrand curves in Galilean 4-space is introduced and the characterization of the generalized Bertrand curves is obtained. Furthermore, it is proved that no special curve is a classical Bertrand curve in Galilean 4-space such that the notion of classical Bertrand curve is definite only in three-dimensional spaces.

MSC:

53A04 Curves in Euclidean and related spaces
Full Text: DOI

References:

[1] Balgetir, H.; Bektas, M.; Ergüt, M., Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic Journal, 27, 2, 229-236 (2004) · Zbl 1059.53003
[2] Choi, J. H.; Kang, T. H.; Kim, Y. H., Bertrand curves in 3-dimensional space forms, Applied Mathematics and Computation, 219, 3, 1040-1046 (2012) · Zbl 1287.53011 · doi:10.1016/j.amc.2012.07.008
[3] Do Carmo, M. P., Differential Geometry of Curves and Surfaces (1976), Pearson Education · Zbl 0326.53001
[4] Ekmekci, N.; Ilarslan, K., On Bertrand curves and their characterization, Differential Geometry—Dynamical Systems, 3, 2, 17-24 (2001) · Zbl 0995.53014
[5] Matsuda, H.; Yorozu, S., Notes on Bertrand curves, Yokohama Mathematical Journal, 50, 1-2, 41-58 (2003) · Zbl 1066.53007
[6] Nadenik, Z., Bertrand curves in five-dimensional space, Czechoslovak Mathematical Journal, 2, 1, 57-87 (1952) · Zbl 0048.38702
[7] Öğrenmiş, A. O.; Öztekin, H.; Ergüt, M., Bertrand curves in Galilean space and their characterizations, Kragujevac Journal of Mathematics, 32, 139-147 (2009) · Zbl 1224.53019
[8] Yilmaz, S., Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications, International Journal of Physical Sciences, 5, 8, 1284-1289 (2010)
[9] Öztekin, H.; Öğrenmiş, A. O., Normal and rectifying curves in pseudo-Galilean space \(G(1 / 3)\) and their characterizations, Journal of Mathematical and Computational Science, 2, 1, 91-100 (2012)
[10] Ogrenmis, A. O.; Ergut, M.; Bektas, M., On the helices in the Galilean space \(G_3\), Iranian Journal of Science and Technology Transaction A: Science, 31, 2, 177-181 (2007) · Zbl 1244.53012
[11] Ersoy, S.; Inalcik, A., Generalized spacelike Bertrand curves in Minkowski 5-space \(R_1^5\), Quaestiones Mathematicae, 37, 1, 19-29 (2014) · Zbl 1397.53038 · doi:10.2989/16073606.2013.779967
[12] Divjak, B.; Milin, Š. Ž., Special curves on ruled surfaces in GALilean and pseudo-GALilean spaces, Acta Mathematica Hungarica, 98, 3, 203-215 (2003) · Zbl 1026.53004 · doi:10.1023/a:1022821824927
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.