Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 72 Sayı: 1, 159 - 168, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1074682

Öz

Kaynakça

  • Neill, B. O., Elementary Differential Geometry, Academic Press New York and London, 1966.
  • Ergün, E., Çalışkan, M., Ruled surface pair generated by a curve and its natural lift in $R^3$, Pure Mathematical Sciences, 1 (2012), 75-80.
  • Izumiya, S., Takeuchi, N., Special curves and ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 44 (1) (2003), 203-212.
  • Karaca, E., Çalışkan, M., Ruled surfaces and tangent bundle of pseudo-sphere of natural lift curves, Journal of Science and Arts, 52 (3) (2020), 573-586. https://doi.org/10.35378/gujs.588496
  • Kim, Y. H., Yoon, D. W., Classification of ruled surfaces in Minkowski 3-Spaces, Journal of Geometry and Physics, 49(1) (2004), 89-100. https://doi.org/10.1016/S0393-0440(03)00084-6
  • Yıldız, Ö. G., Akyiğit, M., Tosun, M., On the trajectory ruled surfaces of framed base curves in the Euclidean Space, Mathematical Methods in the Applied Sciences, 44 (9) (2021), 7463-7470. https://doi.org/10.1002/mma.6267
  • Hathout, F., Bekar, M., Yaylı, Y., Ruled surfaces and tangent bundle of unit 2-sphere, International Journal of Geometric Methods in Modern Physics, 14 (10) (2017), 1750145. https://doi.org/10.1142/S0219887817501456
  • Şentürk, G. Y., Yüce, S., Bertrand offsets of ruled surfaces with Darboux frame, Results in Mathematics, 72 (2017), 1151-1159. https://doi.org/10.1007/s00025-016-0571-6
  • Thorpe, J. A., Elementary Topics in Differential Geometry, Springer Verlag, New York, Heidelberg-Berlin, 1979.
  • Carmo, M. D., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1976.
  • Izumiya, S., Takeuchi, N., Singularities of ruled surfaces in $R^3$, Math. Proc. Camb. Phil. Soc., 130(1) (2001), 1-11. https://doi.org/10.1017/S0305004100004643
  • Perez-Diaz, S., Blasco, A., On the computation of singularities of parametrized ruled surfaces, Advances in Applied Mathematics, 110 (2019), 270-298. https://doi.org/10.1016/j.aam.2019.07.005
  • Martins, R., Nuno-Ballesteros, J. J., Finitely determined singularities of ruled surfaces in R3, Math. Proc. Camb. Phil. Soc., 147 (2009), 701-733. https://doi.org/10.1017/S0305004109002618
  • Jia, X., Chen, F., Deng, J., Computing self-intersection curves of rational ruled surfaces, Computer Aided Geometric Design, 26 (3) (2009), 287-299. https://doi.org/10.1016/j.cagd.2008.09.005
  • Alghanemi, A., On geometry of ruled surfaces generated by the spherical indicatrices of a regular space curve II, International Journal of Algebra, 10 (4) (2016), 193-205. https://doi.org/10.12988/ija.2016.6321
  • Mond, D., Singularities of the tangent developable surface of a space curve, The Quarterly Journal of Mathematics, 40 (1) (1989), 79-91. https://doi.org/10.1093/qmath/40.1.79
  • Lancret, M. A., Memoire sur les courbes a double courbure, Memoires presentes a l’Institut 1, 1806.

B-Lift curves and its ruled surfaces

Yıl 2023, Cilt: 72 Sayı: 1, 159 - 168, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1074682

Öz

In this paper, we have described the B-Lift curve in Euclidean space as a curve obtained by combining the endpoints of the binormal vector of a unit speed curve. Subsequently, we have explored the Frenet frames of the B-Lift curves. Moreover, we have introduced the tangent, normal and binormal surfaces of the B-Lift curve and examined the geometric invariants of these surfaces. Finally, we have investigated the singularities of these surface and visualized the surfaces with MATLAB program.

Kaynakça

  • Neill, B. O., Elementary Differential Geometry, Academic Press New York and London, 1966.
  • Ergün, E., Çalışkan, M., Ruled surface pair generated by a curve and its natural lift in $R^3$, Pure Mathematical Sciences, 1 (2012), 75-80.
  • Izumiya, S., Takeuchi, N., Special curves and ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 44 (1) (2003), 203-212.
  • Karaca, E., Çalışkan, M., Ruled surfaces and tangent bundle of pseudo-sphere of natural lift curves, Journal of Science and Arts, 52 (3) (2020), 573-586. https://doi.org/10.35378/gujs.588496
  • Kim, Y. H., Yoon, D. W., Classification of ruled surfaces in Minkowski 3-Spaces, Journal of Geometry and Physics, 49(1) (2004), 89-100. https://doi.org/10.1016/S0393-0440(03)00084-6
  • Yıldız, Ö. G., Akyiğit, M., Tosun, M., On the trajectory ruled surfaces of framed base curves in the Euclidean Space, Mathematical Methods in the Applied Sciences, 44 (9) (2021), 7463-7470. https://doi.org/10.1002/mma.6267
  • Hathout, F., Bekar, M., Yaylı, Y., Ruled surfaces and tangent bundle of unit 2-sphere, International Journal of Geometric Methods in Modern Physics, 14 (10) (2017), 1750145. https://doi.org/10.1142/S0219887817501456
  • Şentürk, G. Y., Yüce, S., Bertrand offsets of ruled surfaces with Darboux frame, Results in Mathematics, 72 (2017), 1151-1159. https://doi.org/10.1007/s00025-016-0571-6
  • Thorpe, J. A., Elementary Topics in Differential Geometry, Springer Verlag, New York, Heidelberg-Berlin, 1979.
  • Carmo, M. D., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1976.
  • Izumiya, S., Takeuchi, N., Singularities of ruled surfaces in $R^3$, Math. Proc. Camb. Phil. Soc., 130(1) (2001), 1-11. https://doi.org/10.1017/S0305004100004643
  • Perez-Diaz, S., Blasco, A., On the computation of singularities of parametrized ruled surfaces, Advances in Applied Mathematics, 110 (2019), 270-298. https://doi.org/10.1016/j.aam.2019.07.005
  • Martins, R., Nuno-Ballesteros, J. J., Finitely determined singularities of ruled surfaces in R3, Math. Proc. Camb. Phil. Soc., 147 (2009), 701-733. https://doi.org/10.1017/S0305004109002618
  • Jia, X., Chen, F., Deng, J., Computing self-intersection curves of rational ruled surfaces, Computer Aided Geometric Design, 26 (3) (2009), 287-299. https://doi.org/10.1016/j.cagd.2008.09.005
  • Alghanemi, A., On geometry of ruled surfaces generated by the spherical indicatrices of a regular space curve II, International Journal of Algebra, 10 (4) (2016), 193-205. https://doi.org/10.12988/ija.2016.6321
  • Mond, D., Singularities of the tangent developable surface of a space curve, The Quarterly Journal of Mathematics, 40 (1) (1989), 79-91. https://doi.org/10.1093/qmath/40.1.79
  • Lancret, M. A., Memoire sur les courbes a double courbure, Memoires presentes a l’Institut 1, 1806.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Anıl Altınkaya 0000-0003-2382-6596

Mustafa Çalışkan 0000-0003-1354-4763

Yayımlanma Tarihi 30 Mart 2023
Gönderilme Tarihi 16 Şubat 2022
Kabul Tarihi 25 Ağustos 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 1

Kaynak Göster

APA Altınkaya, A., & Çalışkan, M. (2023). B-Lift curves and its ruled surfaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 159-168. https://doi.org/10.31801/cfsuasmas.1074682
AMA Altınkaya A, Çalışkan M. B-Lift curves and its ruled surfaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2023;72(1):159-168. doi:10.31801/cfsuasmas.1074682
Chicago Altınkaya, Anıl, ve Mustafa Çalışkan. “B-Lift Curves and Its Ruled Surfaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 1 (Mart 2023): 159-68. https://doi.org/10.31801/cfsuasmas.1074682.
EndNote Altınkaya A, Çalışkan M (01 Mart 2023) B-Lift curves and its ruled surfaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 159–168.
IEEE A. Altınkaya ve M. Çalışkan, “B-Lift curves and its ruled surfaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 1, ss. 159–168, 2023, doi: 10.31801/cfsuasmas.1074682.
ISNAD Altınkaya, Anıl - Çalışkan, Mustafa. “B-Lift Curves and Its Ruled Surfaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (Mart 2023), 159-168. https://doi.org/10.31801/cfsuasmas.1074682.
JAMA Altınkaya A, Çalışkan M. B-Lift curves and its ruled surfaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:159–168.
MLA Altınkaya, Anıl ve Mustafa Çalışkan. “B-Lift Curves and Its Ruled Surfaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 1, 2023, ss. 159-68, doi:10.31801/cfsuasmas.1074682.
Vancouver Altınkaya A, Çalışkan M. B-Lift curves and its ruled surfaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):159-68.

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

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