On Rectifying Slant Curves in Galilean Space
Year 2023,
Volume: 11 Issue: 1, 46 - 51, 30.04.2023
Mustafa Dede
,
Cumali Ekici
,
Mahmut Koçak
Abstract
In this paper, we study rectifying slant curves in three-dimensional Galilean space. Further geometric properties of rectifying slant curves are also presented in Galilean space. Moreover, we obtain a admissible family of rectifying slant helices for a special case. Consequently, an example is constructed and plotted.
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Mustafa Dede et al. 11
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Year 2023,
Volume: 11 Issue: 1, 46 - 51, 30.04.2023
Mustafa Dede
,
Cumali Ekici
,
Mahmut Koçak
References
- [1] Ali T. Ahmad, Position vectors of slant helices in Euclidean space EJournal of the Egyp-tian Mathematical Society, 20 (1), 1-6, 2012.
- [2] Altunkaya, B., Aksoyak, F.K., Kula, L. and Aytekin, C., On Rectifying Slant Helices in Euclidean 3-Space, Konuralp Journal of Mathematics,
4(2), 17-24, 2016.
- [3] Altunkaya, B. and Kula, L., On Timelike Rectifying Slant Helices
in Minkowski 3-Space, International Electronic Journal of Geometry, 11(1),
17-25, 2018.
- [4] Deshmukh, S., Chen, B.Y. and Alshammari, S.H., On rectifying curves
in Euclidean 3-space,Turk J Math, 42, 609-620, 2018.
- [5] Chen, B.Y., When does the position vector of a space curve always lie
in its rectifying plane?, Amer. Math. Monthly, 110, 147-152, 2003.
- [6] Chen, B.Y., Dillen, F. Rectifying curves as centrodes and extremal
curves, Bull. Inst. Math.Academia Sinica, 33 (2), 77-90, 2005.
- [7] Izumiya S., Takeuchi N., New special curves and developable surfaces,
Turk. J. Math. 28, 153-163, 2004.
- [8] Izumiya S. and Takeuchi N., Generic properties of helices and Bertrand
curves, J. Geom. 74, 97-109, 2002.
- [9] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix,
Applied Mathematics and Computation, 169, 600-607, 2005.
- [10] Kula, L., Ekmekci, N. Yayl, Y. and Ilarslan, K., Characterizations of
slant helices in Euclidean 3-space, Turkish J. Math. 34 (2), 261273, 2010.
Mustafa Dede et al. 11
- [11] Milin-Sipus, Z., Ruled Weingarten surfaces in Galilean space, Periodica Mathematica Hungarica, 56 (2), 213-225, 2008.
- [12] OíNeill B., Elementary Di§erential Geometry, Academic Press, 2006.
- [13] ÷grenmi¸s, A., Erg¸t, M. and Bekta¸s, M., On the Helices in the º
Galilean Space G3; Iranian Journal of Science & Technology, Transaction A,
Printed in The Islamic Republic of Iran, 31 (A2), 2007.
- [14] Rˆschel, O., Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, 1984.
- [15] Struik D.J., Lectures on Classical Di§erential Geometry, Dover, 1961.
- [16] Yaglom, I.M., A Simple Non-Euclidean Geometry and Its Physical
Basis, Springer-Verlag New York Inc., 1979