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Tzitzeica curves with q-frame in three-dimensional Minkowski space

Yıl 2024, Cilt: 73 Sayı: 4, 957 - 968, 30.12.2024

Gul Ugur Kaymanlı , Gamze Nur Şen , Cumali Ekici

https://doi.org/10.31801/cfsuasmas.1365949

Öz

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.

Anahtar Kelimeler

Curvatures spherical curves Tzitzeica curves

Kaynakça

  • 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.

Yıl 2024, Cilt: 73 Sayı: 4, 957 - 968, 30.12.2024

Gul Ugur Kaymanlı , Gamze Nur Şen , Cumali Ekici

https://doi.org/10.31801/cfsuasmas.1365949

Öz

Kaynakça

  • 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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Research Article
Yazarlar

Gul Ugur Kaymanlı 0000-0003-4932-894X

Gamze Nur Şen 0000-0001-5687-4231

Cumali Ekici 0000-0002-3247-5727

Yayımlanma Tarihi 30 Aralık 2024
Gönderilme Tarihi 25 Eylül 2023
Kabul Tarihi 1 Temmuz 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 73 Sayı: 4

Kaynak Göster

APA Ugur Kaymanlı, G., Şen, G. N., & Ekici, C. (2024). Tzitzeica curves with q-frame in three-dimensional Minkowski space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 957-968. https://doi.org/10.31801/cfsuasmas.1365949
AMA Ugur Kaymanlı G, Şen GN, Ekici C. Tzitzeica curves with q-frame in three-dimensional Minkowski space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2024;73(4):957-968. doi:10.31801/cfsuasmas.1365949
Chicago Ugur Kaymanlı, Gul, Gamze Nur Şen, ve Cumali Ekici. “Tzitzeica Curves With Q-Frame in Three-Dimensional Minkowski Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, sy. 4 (Aralık 2024): 957-68. https://doi.org/10.31801/cfsuasmas.1365949.
EndNote Ugur Kaymanlı G, Şen GN, Ekici C (01 Aralık 2024) Tzitzeica curves with q-frame in three-dimensional Minkowski space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 957–968.
IEEE G. Ugur Kaymanlı, G. N. Şen, ve C. Ekici, “Tzitzeica curves with q-frame in three-dimensional Minkowski space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 73, sy. 4, ss. 957–968, 2024, doi: 10.31801/cfsuasmas.1365949.
ISNAD Ugur Kaymanlı, Gul vd. “Tzitzeica Curves With Q-Frame in Three-Dimensional Minkowski Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (Aralık 2024), 957-968. https://doi.org/10.31801/cfsuasmas.1365949.
JAMA Ugur Kaymanlı G, Şen GN, Ekici C. Tzitzeica curves with q-frame in three-dimensional Minkowski space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:957–968.
MLA Ugur Kaymanlı, Gul vd. “Tzitzeica Curves With Q-Frame in Three-Dimensional Minkowski Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 73, sy. 4, 2024, ss. 957-68, doi:10.31801/cfsuasmas.1365949.
Vancouver Ugur Kaymanlı G, Şen GN, Ekici C. Tzitzeica curves with q-frame in three-dimensional Minkowski space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(4):957-68.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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