Research Article
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Year 2023, , 78 - 88, 30.06.2023
https://doi.org/10.33401/fujma.1218966

Abstract

References

  • [1] P. Cermelli, A. J. Di Scala, Constant angle surfaces in liquid crystals, Philos. Mag., 87 (2007), 1871-1888.
  • [2] M. I. Munteanu, A. I. Nistor, A new approach on constant angle surfaces in E3, Turkish J. Math., 33(2) (2009), 1-10.
  • [3] A. I. Nistor, Certain constant angle surfaces constructed on curves, Int. Electron. J. Geom., 4 (2011), 79-87.
  • [4] S. Özkaldı, Y. Yaylı, Constant angle surfaces and curves in E3, Int. Electron. J. Geom., 4(1) (2011), 70-78.
  • [5] A. T. Ali, A constant angle ruled surfaces, Int. Electron. J. Geom., 7(1) (2018), 69-80.
  • [6] C. Y. Li, C. G. Zhu, Construction of the spacelike constant angle surface family in Minkowski 3􀀀space, AIMS Math., 5(6) (2020), 6341-6354.
  • [7] S. Özkaldı Karakuş, Certain constant angle surfaces constructed on curves in Minkowski 3􀀀space, Int. Electron. J. Geom., 11(1) (2018), 37-47.
  • [8] R. Lopez, M. I. Munteanu, Constant angle surfaces in Minkowski space, Bull. Belg. Math. Soc. Simon Stevin, 18(2) (2011), 271-286.
  • [9] A. T. Ali, Non-lightlike constant angle ruled surfaces in Minkowski 3-space, J. Geom. Phys., 157 (2020), 103833.
  • [10] F. Güler, G. Şaffak, E. Kasap, Timelike constant angle surfaces in Minkowski space R31, Int. J. Contemp. Math. Sciences, 6(44) (2011), 2189-2200.
  • [11] G. U. Kaymanlı, C. Ekici, Y. Ünlütürk, Constant angle ruled surfaces due to the Bishop frame in Minkowski 3-space, J. Sci. Arts, 22(1) (2022), 105-114.
  • [12] F. Dillen, J. Fastenakels, J. Van de Veken, L. Vrancken, Constant angle surfaces in S2 R, Monatsh. Math., 152 (2007), 89-96.
  • [13] S. Özkaldı Karakuş, Quaternionic approach on constant angle surfaces in S2 R, Appl. Math. E-Notes, 19 (2019), 497-506.
  • [14] F. Dillen, M. I. Munteanu, Constant angle surfaces in H2 R, Bull. Braz. Math. Soc., 40 (2009), 85-97.
  • [15] J. Fastenakels, M. I. Munteanu, J. Van Der Veken, Constant angle surfaces in the Heisenberg group, Acta Math. Sin. (Engl. Ser.), 27(4) (2011), 747-756.
  • [16] I. I. Onnis, P. Piu, Constant angle surfaces in the Lorentzian Heisenberg group, Arch. Math., 109 (2017), 575-589.
  • [17] F. Doğan, Y. Yayli, On isophote curves and their characterizations, Turkish J. Math., 39(5) (2015), 650-664.
  • [18] C. E. Ordo˜nez, E. Blotta, J. I. Pastore, Isophote based low computing power eye detection embedded system, IEEE Latin America Transactions, 18(02) (2020), 336-343.
  • [19] S. Datta, N. Chaki, B. Modak, A novel technique to detect caries lesion using isophote concepts, IRBM, 40(3) (2019), 174-182.
  • [20] T. Körpınar, R. C. Demirkol, Z. K¨orpınar, Polarization of propagated light with optical solitons along the fiber in de-sitter space S21, Optik, 226 (2021), 165872.
  • [21] T. Körpinar, R. C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D Riemannian manifold with Bishop equations, Optik, 200 (2020), 163334.
  • [22] Z. Özdemir, A new calculus for the treatment of Rytov’s law in the optical fiber, Optik, 216 (2020), 164892.
  • [23] B. Yılmaz, A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus, Optik, 247 (2021), 168026.
  • [24] Z. Özdemir, F. N. Ekmekçi, Electromagnetic curves and Rytov curves based on the hyperbolic split quaternion algebra, Optik, 251 (2022), 168359.
  • [25] B. O’neill, Semi-Riemannian Geometry with Applications to Relativity, Academic press, Los Angeles, 1983.
  • [26] D. J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Publishing, New York, 1961.
  • [27] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [28] H. H. Hacısalihoğlu, Diferensiyel Geometri, ˙Inonu University, Faculty of Arts and Sciences Publications, Malatya, 1983.
  • [29] A. Sabuncuoğlu, Diferensiyel Geometri, Nobel Publications, Ankara, 2004.
  • [30] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs., New Jersey, 1976.
  • [31] M. Özdemir, Diferansiyel Geometri, Altı Nokta Publications, I˙zmir, 2020.
  • [32] S. Izumiya, Generating families of developable surfaces in R3, Hokkaido Univ. Pre. Series in Mathematics, 512 (2001), 1-18.
  • [33] S. Izumiya, N. Takeuchi, Singularities of ruled surfaces in R3, In Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 130(1) (2001), 1-11.

Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$

Year 2023, , 78 - 88, 30.06.2023
https://doi.org/10.33401/fujma.1218966

Abstract

In this study, for the first time, a method is given for a developable ruled surface to be a constant angle ruled surface. The general equations of constant angle surfaces have been shown in the studies done so far. In this study, a new method is given on how to obtain a constant angled surface when any constant direction is given in Minkowski $3-$space.

References

  • [1] P. Cermelli, A. J. Di Scala, Constant angle surfaces in liquid crystals, Philos. Mag., 87 (2007), 1871-1888.
  • [2] M. I. Munteanu, A. I. Nistor, A new approach on constant angle surfaces in E3, Turkish J. Math., 33(2) (2009), 1-10.
  • [3] A. I. Nistor, Certain constant angle surfaces constructed on curves, Int. Electron. J. Geom., 4 (2011), 79-87.
  • [4] S. Özkaldı, Y. Yaylı, Constant angle surfaces and curves in E3, Int. Electron. J. Geom., 4(1) (2011), 70-78.
  • [5] A. T. Ali, A constant angle ruled surfaces, Int. Electron. J. Geom., 7(1) (2018), 69-80.
  • [6] C. Y. Li, C. G. Zhu, Construction of the spacelike constant angle surface family in Minkowski 3􀀀space, AIMS Math., 5(6) (2020), 6341-6354.
  • [7] S. Özkaldı Karakuş, Certain constant angle surfaces constructed on curves in Minkowski 3􀀀space, Int. Electron. J. Geom., 11(1) (2018), 37-47.
  • [8] R. Lopez, M. I. Munteanu, Constant angle surfaces in Minkowski space, Bull. Belg. Math. Soc. Simon Stevin, 18(2) (2011), 271-286.
  • [9] A. T. Ali, Non-lightlike constant angle ruled surfaces in Minkowski 3-space, J. Geom. Phys., 157 (2020), 103833.
  • [10] F. Güler, G. Şaffak, E. Kasap, Timelike constant angle surfaces in Minkowski space R31, Int. J. Contemp. Math. Sciences, 6(44) (2011), 2189-2200.
  • [11] G. U. Kaymanlı, C. Ekici, Y. Ünlütürk, Constant angle ruled surfaces due to the Bishop frame in Minkowski 3-space, J. Sci. Arts, 22(1) (2022), 105-114.
  • [12] F. Dillen, J. Fastenakels, J. Van de Veken, L. Vrancken, Constant angle surfaces in S2 R, Monatsh. Math., 152 (2007), 89-96.
  • [13] S. Özkaldı Karakuş, Quaternionic approach on constant angle surfaces in S2 R, Appl. Math. E-Notes, 19 (2019), 497-506.
  • [14] F. Dillen, M. I. Munteanu, Constant angle surfaces in H2 R, Bull. Braz. Math. Soc., 40 (2009), 85-97.
  • [15] J. Fastenakels, M. I. Munteanu, J. Van Der Veken, Constant angle surfaces in the Heisenberg group, Acta Math. Sin. (Engl. Ser.), 27(4) (2011), 747-756.
  • [16] I. I. Onnis, P. Piu, Constant angle surfaces in the Lorentzian Heisenberg group, Arch. Math., 109 (2017), 575-589.
  • [17] F. Doğan, Y. Yayli, On isophote curves and their characterizations, Turkish J. Math., 39(5) (2015), 650-664.
  • [18] C. E. Ordo˜nez, E. Blotta, J. I. Pastore, Isophote based low computing power eye detection embedded system, IEEE Latin America Transactions, 18(02) (2020), 336-343.
  • [19] S. Datta, N. Chaki, B. Modak, A novel technique to detect caries lesion using isophote concepts, IRBM, 40(3) (2019), 174-182.
  • [20] T. Körpınar, R. C. Demirkol, Z. K¨orpınar, Polarization of propagated light with optical solitons along the fiber in de-sitter space S21, Optik, 226 (2021), 165872.
  • [21] T. Körpinar, R. C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D Riemannian manifold with Bishop equations, Optik, 200 (2020), 163334.
  • [22] Z. Özdemir, A new calculus for the treatment of Rytov’s law in the optical fiber, Optik, 216 (2020), 164892.
  • [23] B. Yılmaz, A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus, Optik, 247 (2021), 168026.
  • [24] Z. Özdemir, F. N. Ekmekçi, Electromagnetic curves and Rytov curves based on the hyperbolic split quaternion algebra, Optik, 251 (2022), 168359.
  • [25] B. O’neill, Semi-Riemannian Geometry with Applications to Relativity, Academic press, Los Angeles, 1983.
  • [26] D. J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Publishing, New York, 1961.
  • [27] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [28] H. H. Hacısalihoğlu, Diferensiyel Geometri, ˙Inonu University, Faculty of Arts and Sciences Publications, Malatya, 1983.
  • [29] A. Sabuncuoğlu, Diferensiyel Geometri, Nobel Publications, Ankara, 2004.
  • [30] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs., New Jersey, 1976.
  • [31] M. Özdemir, Diferansiyel Geometri, Altı Nokta Publications, I˙zmir, 2020.
  • [32] S. Izumiya, Generating families of developable surfaces in R3, Hokkaido Univ. Pre. Series in Mathematics, 512 (2001), 1-18.
  • [33] S. Izumiya, N. Takeuchi, Singularities of ruled surfaces in R3, In Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 130(1) (2001), 1-11.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Aykut Has 0000-0003-0658-9365

Beyhan Yılmaz 0000-0002-5091-3487

Yusuf Yaylı 0000-0003-4398-3855

Early Pub Date May 25, 2023
Publication Date June 30, 2023
Submission Date December 14, 2022
Acceptance Date April 18, 2023
Published in Issue Year 2023

Cite

APA Has, A., Yılmaz, B., & Yaylı, Y. (2023). Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$. Fundamental Journal of Mathematics and Applications, 6(2), 78-88. https://doi.org/10.33401/fujma.1218966
AMA Has A, Yılmaz B, Yaylı Y. Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$. Fundam. J. Math. Appl. June 2023;6(2):78-88. doi:10.33401/fujma.1218966
Chicago Has, Aykut, Beyhan Yılmaz, and Yusuf Yaylı. “Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$”. Fundamental Journal of Mathematics and Applications 6, no. 2 (June 2023): 78-88. https://doi.org/10.33401/fujma.1218966.
EndNote Has A, Yılmaz B, Yaylı Y (June 1, 2023) Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$. Fundamental Journal of Mathematics and Applications 6 2 78–88.
IEEE A. Has, B. Yılmaz, and Y. Yaylı, “Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$”, Fundam. J. Math. Appl., vol. 6, no. 2, pp. 78–88, 2023, doi: 10.33401/fujma.1218966.
ISNAD Has, Aykut et al. “Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$”. Fundamental Journal of Mathematics and Applications 6/2 (June 2023), 78-88. https://doi.org/10.33401/fujma.1218966.
JAMA Has A, Yılmaz B, Yaylı Y. Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$. Fundam. J. Math. Appl. 2023;6:78–88.
MLA Has, Aykut et al. “Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 2, 2023, pp. 78-88, doi:10.33401/fujma.1218966.
Vancouver Has A, Yılmaz B, Yaylı Y. Constant Angle Ruled Surfaces in $\mathbb{E}^{3}_1$. Fundam. J. Math. Appl. 2023;6(2):78-8.

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