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Year 2021, , 379 - 387, 31.12.2021
https://doi.org/10.47000/tjmcs.969243

Abstract

References

  • [1] Bishop, R.L., There is more than one way to Frame a curve, American Mathematical Monthly, 82(3)(1975), 246–251.
  • [2] Capın, R., Minkowski Uzayında Küresel Gösterge Eğrileri, Yüksek Lisans Tezi, Gaziantep Üniversitesi Fen Bilimleri Enstitüsü, Gaziantep, 77p, 2016.
  • [3] Dede, M., A new representation of tubular surfaces, Houston J. Math. 45(3)(2019), 707—720.
  • [4] Farouki, R.T., Han, C.Y., Manni, C., Sestini, A., Characterization and construction of helical polynomial space curves, Journal of Computational and Applied Mathematics 162(2004), 365-–392.
  • [5] Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü , Manisa, 65p, 2018.
  • [6] Hacısalihogğlu, H.H., Diferansiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Ankara, 1993.
  • [7] Kula, L., Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput., 169(1)(2005), 600–607.
  • [8] Larson, R., Elemantary Linear Algebra, The Pennsylvania State University, Boston, 2012.
  • [9] O’Neill, B., Elementary Diferential Geometry. New York, Academic Press Inc., 1966.
  • [10] Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in E3, International Journal of the Physical Sciences, 7(16)(2012), 2414–2421.
  • [11] Şenyurt, S., Özgüner, Z., Bertrand eğri çiftinin küresel göstergelerinin geodezik eğrilikleri ve tabii liftleri, Ordu Üniv. Bil. Tek. Derg., 3(2)(2013), 58–81.
  • [12] Yılmaz, S., Özyılmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. Şt. Univ. Ovidius Constanta., 18(2)(2010), 337–354.

Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame

Year 2021, , 379 - 387, 31.12.2021
https://doi.org/10.47000/tjmcs.969243

Abstract

In this study, the spherical indicatrices of Flc frame vectors were defined on unit sphere. The arc length parameters and the Frenet vectors of these indicatrix curves were calculated, as well. Last, we have provided the geodesic curvatures according to both Euclidean space $E^3$ and unit sphere $S^2$.

References

  • [1] Bishop, R.L., There is more than one way to Frame a curve, American Mathematical Monthly, 82(3)(1975), 246–251.
  • [2] Capın, R., Minkowski Uzayında Küresel Gösterge Eğrileri, Yüksek Lisans Tezi, Gaziantep Üniversitesi Fen Bilimleri Enstitüsü, Gaziantep, 77p, 2016.
  • [3] Dede, M., A new representation of tubular surfaces, Houston J. Math. 45(3)(2019), 707—720.
  • [4] Farouki, R.T., Han, C.Y., Manni, C., Sestini, A., Characterization and construction of helical polynomial space curves, Journal of Computational and Applied Mathematics 162(2004), 365-–392.
  • [5] Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü , Manisa, 65p, 2018.
  • [6] Hacısalihogğlu, H.H., Diferansiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Ankara, 1993.
  • [7] Kula, L., Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput., 169(1)(2005), 600–607.
  • [8] Larson, R., Elemantary Linear Algebra, The Pennsylvania State University, Boston, 2012.
  • [9] O’Neill, B., Elementary Diferential Geometry. New York, Academic Press Inc., 1966.
  • [10] Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in E3, International Journal of the Physical Sciences, 7(16)(2012), 2414–2421.
  • [11] Şenyurt, S., Özgüner, Z., Bertrand eğri çiftinin küresel göstergelerinin geodezik eğrilikleri ve tabii liftleri, Ordu Üniv. Bil. Tek. Derg., 3(2)(2013), 58–81.
  • [12] Yılmaz, S., Özyılmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. Şt. Univ. Ovidius Constanta., 18(2)(2010), 337–354.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Kebire Hilal Ayvacı 0000-0002-5114-5475

Süleyman Şenyurt 0000-0003-1097-5541

Davut Canlı 0000-0003-0405-9969

Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Ayvacı, K. H., Şenyurt, S., & Canlı, D. (2021). Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. Turkish Journal of Mathematics and Computer Science, 13(2), 379-387. https://doi.org/10.47000/tjmcs.969243
AMA Ayvacı KH, Şenyurt S, Canlı D. Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. TJMCS. December 2021;13(2):379-387. doi:10.47000/tjmcs.969243
Chicago Ayvacı, Kebire Hilal, Süleyman Şenyurt, and Davut Canlı. “Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 379-87. https://doi.org/10.47000/tjmcs.969243.
EndNote Ayvacı KH, Şenyurt S, Canlı D (December 1, 2021) Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. Turkish Journal of Mathematics and Computer Science 13 2 379–387.
IEEE K. H. Ayvacı, S. Şenyurt, and D. Canlı, “Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame”, TJMCS, vol. 13, no. 2, pp. 379–387, 2021, doi: 10.47000/tjmcs.969243.
ISNAD Ayvacı, Kebire Hilal et al. “Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 379-387. https://doi.org/10.47000/tjmcs.969243.
JAMA Ayvacı KH, Şenyurt S, Canlı D. Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. TJMCS. 2021;13:379–387.
MLA Ayvacı, Kebire Hilal et al. “Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 379-87, doi:10.47000/tjmcs.969243.
Vancouver Ayvacı KH, Şenyurt S, Canlı D. Some Characterizations of Spherical Indicatrix Curves Generated by Flc Frame. TJMCS. 2021;13(2):379-87.