Research Article
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New Kind Frenet Curves in Minkowski Space

Year 2021, Volume: 2 Issue: 2, 70 - 82, 31.07.2021

Abstract

In this study, we define new vector fields along a Frenet curve with nonvanishing curvatures in 4-dimensional Minkowski space R^4_1 . By using these vector fields we obtain some new planes and curves. We show that these planes play the role of the Darboux vector. We characterized that, osculating curves of the first kind and rectifying curves in Minkowski space R^4_1 can be given as space curves whose position vectors always lie in a two-dimensional subspace.

References

  • [1] Ali A.T., Önder M., Some characterizations of rectifying spacelike curves in the Minkowski space-time, Global Journal of Science Frontier Research Mathematics, 12(1), 2249-4626, 2012.
  • [2] Camcı Ç., İlarslan K., Kula L., Hacısalihoğlu H.H., Harmonic curvatures and generalized helices in E^n , Chaos, Solitons and Fractals, 40(5), 2590-2596, 2009.
  • [3] Düldül M., Vector fields and planes in E4 which play the role of Darboux vector, Turkish Journal of Mathematics, 44, 274-283, 2020.
  • [4] Izumiya S., Takeuchi N., New special curves and developable surfaces, Turkish Journal of Mathematics, 28(2), 153-163, 2004.
  • [5] İlarslan K., Boyacıoğlu Ö., Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos, Solitions and Fractals, 38, 1383-1389, 2008.
  • [6] İlarslan K., Nesovic E., Some characterizations of null osculating curves in the Minkowski space-time, Proceedings of the Estonian Academy of Sciences, 61(I), 1-8, 2012.
  • [7] İlarslan K., Nesovic E., Petrovic-Torgasev M., Some characterizations of rectifying curves in Minkowski 3-space, Novi Sad Journal of Mathematics, 33(2), 23-32, 2003.
  • [8] Keleş S., Yüksel Perktaş S., Kılıç E., Biharmonic curves in LP-Sasakian manifolds, Bulletin of the Malaysian Mathematical Society, 33(2), 325-344, 2010.
  • [9] Öztürk G., Gürpınar S., Arslan K., A new characterization of curves in Euclidean 4-Space E^4 , Buletinul Academiei de Ştiinte a Republicii Moldova. Matematica, 83(1), 39-50, 2017.
  • [10] Walrave J., Curves and Surfaces in Minkowski Space, Doctoral Thesis, K.U. Leuven, Fac. of Science, 1995.
  • [11] Williams M.Z., Stein F.M., A triple product of vectors in four-space, Mathematics Magazine, 37(4), 230-235, 1964.
  • [12] Yaylı Y., Gök İ., Hacısalihoğlu H.H., Extended rectifying curves as new kind of modified Darboux vectors, TWMS Journal of Pure and Applied Mathematics, 9(1), 18-31, 2018.
Year 2021, Volume: 2 Issue: 2, 70 - 82, 31.07.2021

Abstract

References

  • [1] Ali A.T., Önder M., Some characterizations of rectifying spacelike curves in the Minkowski space-time, Global Journal of Science Frontier Research Mathematics, 12(1), 2249-4626, 2012.
  • [2] Camcı Ç., İlarslan K., Kula L., Hacısalihoğlu H.H., Harmonic curvatures and generalized helices in E^n , Chaos, Solitons and Fractals, 40(5), 2590-2596, 2009.
  • [3] Düldül M., Vector fields and planes in E4 which play the role of Darboux vector, Turkish Journal of Mathematics, 44, 274-283, 2020.
  • [4] Izumiya S., Takeuchi N., New special curves and developable surfaces, Turkish Journal of Mathematics, 28(2), 153-163, 2004.
  • [5] İlarslan K., Boyacıoğlu Ö., Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos, Solitions and Fractals, 38, 1383-1389, 2008.
  • [6] İlarslan K., Nesovic E., Some characterizations of null osculating curves in the Minkowski space-time, Proceedings of the Estonian Academy of Sciences, 61(I), 1-8, 2012.
  • [7] İlarslan K., Nesovic E., Petrovic-Torgasev M., Some characterizations of rectifying curves in Minkowski 3-space, Novi Sad Journal of Mathematics, 33(2), 23-32, 2003.
  • [8] Keleş S., Yüksel Perktaş S., Kılıç E., Biharmonic curves in LP-Sasakian manifolds, Bulletin of the Malaysian Mathematical Society, 33(2), 325-344, 2010.
  • [9] Öztürk G., Gürpınar S., Arslan K., A new characterization of curves in Euclidean 4-Space E^4 , Buletinul Academiei de Ştiinte a Republicii Moldova. Matematica, 83(1), 39-50, 2017.
  • [10] Walrave J., Curves and Surfaces in Minkowski Space, Doctoral Thesis, K.U. Leuven, Fac. of Science, 1995.
  • [11] Williams M.Z., Stein F.M., A triple product of vectors in four-space, Mathematics Magazine, 37(4), 230-235, 1964.
  • [12] Yaylı Y., Gök İ., Hacısalihoğlu H.H., Extended rectifying curves as new kind of modified Darboux vectors, TWMS Journal of Pure and Applied Mathematics, 9(1), 18-31, 2018.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Müslüm Aykut Akgün 0000-0002-8414-5228

Publication Date July 31, 2021
Published in Issue Year 2021 Volume: 2 Issue: 2

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.