Research Article

On the curvatures of the ruled surfaces of b-lift curves

Volume: 42 Number: 4 December 29, 2021
Anıl Altınkaya *, Mustafa Çalışkan
PDF Download
Cumhuriyet Science Journal Cover Cumhuriyet Science Journal
EN

On the curvatures of the ruled surfaces of b-lift curves

Abstract

In this study, we defined a new curve which is called the B-Lift curve, also obtained the Frenet vectors of the B-Lift curve. The ruled surfaces have been produced by taking base curves B-Lift curves. Moreover, the tangent, normal, and binormal surfaces of the B-Lift curve are introduced. Besides, the Darboux frame of these ruled surfaces is created. The characterizations of these ruled surfaces are also given and the cases of base curves as the asymptotic curve, geodesic curve, principal line are examined. Finally, examples of these ruled surfaces are given and we illustrate them.

Keywords

B-Lift, Natural Lift, Ruled Surface, Darboux Frame, Curvature

References

  1. [1] Carmo M. Do., Differential Geometry of Curves and Surfaces, Prentice- Hall,Inc., Englewood Cliffs, New Jersey, (1976) 1-114.
  2. [2] Mert T., Atçeken M., Some Special Ruled Surfaces in Hyperbolic 3-Space, Konuralp Journal of Mathematics, 9 (2) (2021) 298-309.
  3. [3] Mert T., Atçeken M., Special Ruled Surfaces in de-Sitter 3-Space, Fundamental Journal of Mathematics and Applications 4 (3) (2021) 195-209.
  4. [4] Mert T., Atçeken M., Spacelike Ruled Surfaces in de-Sitter 3-Space, Asian Journal of Mathematics and Computer Research, 27 (4) (2020) 37-53.
  5. [5] 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.
  6. [6] Ergün E., Çalışkan M., Ruled Surface Pair Generated by a Curve and its Natural Lift in R^3, Pure Mathematical Sciences, 1 (2) (2012) 75-80.
  7. [7] Thorpe J. A., Elementary Topics in Differential Geometry, Springer Verlag, New York, Heidelberg-Berlin, (1979) 61.
  8. [8] Izumiya S., Takeuchi N., Special Curves and Ruled Surfaces, Beitrage zur Algebra und Geometric Contributions to Algebra and Geometry, 44 (1) (2003) 203-212.
  9. [9] Lancret M. A., Memoire sur les courbes a double courbure, Memoires presentes a l’Institut, 1 (1) (1806) 416-454.
  10. [10] O’Neill B., Elementary Differential Geometry, Academic Press New York and London, (1966) 42-187.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

December 29, 2021

Submission Date

April 5, 2021

Acceptance Date

October 12, 2021

Published in Issue

Year 2021 Volume: 42 Number: 4

IZ

https://izlik.org/JA48BJ76ML

Cite

RIS / Bibtex
APA
Altınkaya, A., & Çalışkan, M. (2021). On the curvatures of the ruled surfaces of b-lift curves. Cumhuriyet Science Journal, 42(4), 873-877. https://izlik.org/JA48BJ76ML
AMA
1.Altınkaya A, Çalışkan M. On the curvatures of the ruled surfaces of b-lift curves. CSJ. 2021;42(4):873-877. https://izlik.org/JA48BJ76ML
Chicago
Altınkaya, Anıl, and Mustafa Çalışkan. 2021. “On the Curvatures of the Ruled Surfaces of B-Lift Curves”. Cumhuriyet Science Journal 42 (4): 873-77. https://izlik.org/JA48BJ76ML.
EndNote
Altınkaya A, Çalışkan M (December 1, 2021) On the curvatures of the ruled surfaces of b-lift curves. Cumhuriyet Science Journal 42 4 873–877.
IEEE
[1]A. Altınkaya and M. Çalışkan, “On the curvatures of the ruled surfaces of b-lift curves”, CSJ, vol. 42, no. 4, pp. 873–877, Dec. 2021, [Online]. Available: https://izlik.org/JA48BJ76ML
ISNAD
Altınkaya, Anıl - Çalışkan, Mustafa. “On the Curvatures of the Ruled Surfaces of B-Lift Curves”. Cumhuriyet Science Journal 42/4 (December 1, 2021): 873-877. https://izlik.org/JA48BJ76ML.
JAMA
1.Altınkaya A, Çalışkan M. On the curvatures of the ruled surfaces of b-lift curves. CSJ. 2021;42:873–877.
MLA
Altınkaya, Anıl, and Mustafa Çalışkan. “On the Curvatures of the Ruled Surfaces of B-Lift Curves”. Cumhuriyet Science Journal, vol. 42, no. 4, Dec. 2021, pp. 873-7, https://izlik.org/JA48BJ76ML.
Vancouver
1.Anıl Altınkaya, Mustafa Çalışkan. On the curvatures of the ruled surfaces of b-lift curves. CSJ [Internet]. 2021 Dec. 1;42(4):873-7. Available from: https://izlik.org/JA48BJ76ML

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December