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On Rectifying Slant Curves in Galilean Space

Year 2023, Volume: 11 Issue: 1, 46 - 51, 30.04.2023

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.

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
Year 2023, Volume: 11 Issue: 1, 46 - 51, 30.04.2023

Abstract

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
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mustafa Dede

Cumali Ekici

Mahmut Koçak

Publication Date April 30, 2023
Submission Date March 14, 2022
Acceptance Date November 8, 2022
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Dede, M., Ekici, C., & Koçak, M. (2023). On Rectifying Slant Curves in Galilean Space. Konuralp Journal of Mathematics, 11(1), 46-51.
AMA Dede M, Ekici C, Koçak M. On Rectifying Slant Curves in Galilean Space. Konuralp J. Math. April 2023;11(1):46-51.
Chicago Dede, Mustafa, Cumali Ekici, and Mahmut Koçak. “On Rectifying Slant Curves in Galilean Space”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 46-51.
EndNote Dede M, Ekici C, Koçak M (April 1, 2023) On Rectifying Slant Curves in Galilean Space. Konuralp Journal of Mathematics 11 1 46–51.
IEEE M. Dede, C. Ekici, and M. Koçak, “On Rectifying Slant Curves in Galilean Space”, Konuralp J. Math., vol. 11, no. 1, pp. 46–51, 2023.
ISNAD Dede, Mustafa et al. “On Rectifying Slant Curves in Galilean Space”. Konuralp Journal of Mathematics 11/1 (April 2023), 46-51.
JAMA Dede M, Ekici C, Koçak M. On Rectifying Slant Curves in Galilean Space. Konuralp J. Math. 2023;11:46–51.
MLA Dede, Mustafa et al. “On Rectifying Slant Curves in Galilean Space”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 46-51.
Vancouver Dede M, Ekici C, Koçak M. On Rectifying Slant Curves in Galilean Space. Konuralp J. Math. 2023;11(1):46-51.
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