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Year 2023, Volume: 6 Issue: 2, 78 - 88, 30.06.2023

Aykut Has Beyhan Yılmaz Yusuf Yaylı

https://doi.org/10.33401/fujma.1218966
Cited By: 1

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, Volume: 6 Issue: 2, 78 - 88, 30.06.2023

Aykut Has Beyhan Yılmaz Yusuf Yaylı

https://doi.org/10.33401/fujma.1218966
Cited By: 1

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.

Keywords

Constant angle surface Developable ruled surface Isophote curve Optic Singularity Spherical circle

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 Volume: 6 Issue: 2

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 $\mathbb{E}^{3}_1$. FUJMA. 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 $\mathbb{E}^{3}_1$”, FUJMA, 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 $\mathbb{E}^{3}_1$. FUJMA. 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 $\mathbb{E}^{3}_1$. FUJMA. 2023;6(2):78-8.

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