Tzitzeica curves with q-frame in three-dimensional Minkowski space
Year 2024,
Volume: 73 Issue: 4, 957 - 968
Gul Ugur Kaymanlı
,
Gamze Nur Şen
,
Cumali Ekici
Abstract
In this work, both timelike and spacelike Tzitzeica, spherical, and spherical Tzitzeica curves are analyzed in 3-dimensional Minkowski space by using q-frame. Tzitzeica and spherical curves are characterized using spacelike and timelike q-frames within the context of Minkowski three-space, and the theorems concerning spherical Tzitzeica curves are established.
References
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- Yüce, S., Öklid Uzayında Diferansiyel Geometri, Pegem Akademi Yayıncılık, Ankara, 2017.
Year 2024,
Volume: 73 Issue: 4, 957 - 968
Gul Ugur Kaymanlı
,
Gamze Nur Şen
,
Cumali Ekici
References
- Agnew, A. F., Bobe, A., Boskoff, W. G., Suceava, B. D., Tzitzeica curves and surfaces, The Mathematica Journal 12, Wolfram Media, Inc., (2010), 1-18. https://doi.org/10.3888/tmj.12-3
- Akutagawa, K., Nishikawa, S., The Gauss map and space-like surfaces with prescribed mean curvature in Minkowski 3-space, Tohouku Mathematic Journal, 42 (1990), 67-82. https://doi.org/10.2748/tmj/1178227694
- Aydın, M. E., Ergüt, M., Non-null curves of Tzitzeica type in Minkowski 3-space, Romanian J. of Math. Comp. Science, 4(1) (2004), 81-90.
- Bayram, B., Tunç, E., Arslan, K., Öztürk, G., On Tzitzeica curves in Euclidean 3-space, Facta Univ. Ser. Math. Inform., 33(3) (2018), 409-416. https://doi.org/10.22190/FUMI1803409B
- Bobe, A., Boskoff, G., Ciuca, G., Tzitzeica type centro-affine invariants in Minkowski space, An. St. Univ. Ovidius Constanta, 20(2) (2012), 27-34. https://doi.org/10.2478/v10309-012-0037-0
- Bükcü, B., Karacan, M. K., Bishop frame of the spacellike curve with a spacellike principal normal in Minkowski 3 space, Commun. Fac. of Sci. Uni. of Ankara Series A1 Mathematics and Statistics, 57(1) (2008), 13-22. https://doi.org/10.1501/Commua1 0000000185
- Crasmareanu, M., Cylindrical Tzitzeica curves implies forced harmonic oscillators. Balkan J. of Geom. and Its App. 7(1) (2002), 37-42.
- Ekici, C., Tozak, H., Dede, M., Timelike directional tubular surfaces, Journal of Mathematical Analysis, 8(5), (2017), 1-11.
- Eren, K., Ersoy, S., Characterizations of Tzitzeica curves using Bishop frames, Math.Meth.Appl.Sci., (2021),1-14. https://doi.org/10.1002/mma.7483
- Gün Bozok, H., Aykurt Sepet, S., Ergüt, M., Curves of constant breadth according to type-2 Bishop frame in E3. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1) (2017), 206-212. https://doi.org/10.1501/Commua1 0000000790
- Karacan, M. K., Bükcü, B., On the hyperbolic cylindrical Tzitzeica curves in Minkowski 3-space, BA¨U FBE Dergisi, 10(1) (2008), 46-51.
- Karacan, M.K., Bükcü, B., On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space, Sci. Manga, 5 (2009), 44-48.
- Kaymanlı Uğur, G., Dede, M., Ekici, C., Directional spherical indicatrices of timelike space curve, International Journal of Geometric Methods in Modern Physics, 17(11) (2020), 1-15. https://doi.org/10.1142/S0219887820300044
- Kaymanlı Uğur, G., Ekici, C., Evolutions of the Ruled surfaces along a spacelike space curve, Punjab University Journal of Mathematics, 54(4) (2022), 221-232. https://doi.org/10.52280/pujm.2022.540401
- Kaymanlı Uğur, G., Ekici, C., Dede, M., Directional evolution of the Ruled surfaces via the evolution of their directrix using q-frame along a timelike space curve, European Journal of Science and Technology, 20 (2020), 392-396. https://doi.org/10.31590/ejosat.681674
- Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014) 44-107. https://doi.org/10.36890/iejg.594497
- O’Neill, B., Semi-Riemannian Geometry, Academic Press, New York, 1983.
- Özen, K.E., Isbilir, Z., Tosun, M. Characterization of Tzitzeica curves using positional adapted frame, Konuralp J. Math., 10(2) (2022), 260-268.
- Tarım, G., Minkowski Uzayında Yönlü Eğriler Üzerine, Eskişehir Osmangazi Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2016.
- Tzitzeica, G., Sur certaines courbes gauches, Ann. De I’Ec, Normale Sup., 28 (1911), 9-32. https://doi.org/10.24033/asens.632
- Tzitzeica, G., Sur certaines courbes gauches, Ann. De I’Ec, Normale Sup., 42 (1925), 379-390. https://doi.org/10.24033/asens.768
- Uğurlu, H.H., Çalışkan, A., Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi, Celal Bayar Üniversitesi Yayınları, 0006, 2012.
- Ünlütürk, Y., Ekici, C., Ünal, D., A new modelling of timelike q-helices, Honam Mathematical Journal, 45(2) (2023), 231-247. https://doi.org/10.5831/HMJ.2023.45.2.231
- Yüce, S., Öklid Uzayında Diferansiyel Geometri, Pegem Akademi Yayıncılık, Ankara, 2017.