Research Article
Year 2021,
Volume: 42 Issue: 4, 873 - 877, 29.12.2021
Abstract
References
- [1] Carmo M. Do., Differential Geometry of Curves and Surfaces, Prentice- Hall,Inc., Englewood Cliffs, New Jersey, (1976) 1-114.
- [2] Mert T., Atçeken M., Some Special Ruled Surfaces in Hyperbolic 3-Space, Konuralp Journal of Mathematics, 9 (2) (2021) 298-309.
- [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] 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] 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] 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] Thorpe J. A., Elementary Topics in Differential Geometry, Springer Verlag, New York, Heidelberg-Berlin, (1979) 61.
- [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] Lancret M. A., Memoire sur les courbes a double courbure, Memoires presentes a l’Institut, 1 (1) (1806) 416-454.
- [10] O’Neill B., Elementary Differential Geometry, Academic Press New York and London, (1966) 42-187.
- [11] Izumiya S., Otani S., Flat Approximations of Surfaces Along Curves, Demonstratio Mathematica, 48 (2) (2015) 217-241.
Year 2021,
Volume: 42 Issue: 4, 873 - 877, 29.12.2021
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.
References
- [1] Carmo M. Do., Differential Geometry of Curves and Surfaces, Prentice- Hall,Inc., Englewood Cliffs, New Jersey, (1976) 1-114.
- [2] Mert T., Atçeken M., Some Special Ruled Surfaces in Hyperbolic 3-Space, Konuralp Journal of Mathematics, 9 (2) (2021) 298-309.
- [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] 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] 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] 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] Thorpe J. A., Elementary Topics in Differential Geometry, Springer Verlag, New York, Heidelberg-Berlin, (1979) 61.
- [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] Lancret M. A., Memoire sur les courbes a double courbure, Memoires presentes a l’Institut, 1 (1) (1806) 416-454.
- [10] O’Neill B., Elementary Differential Geometry, Academic Press New York and London, (1966) 42-187.
- [11] Izumiya S., Otani S., Flat Approximations of Surfaces Along Curves, Demonstratio Mathematica, 48 (2) (2015) 217-241.
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 29, 2021 |
| Submission Date | April 5, 2021 |
| Acceptance Date | October 12, 2021 |
| Published in Issue | Year 2021Volume: 42 Issue: 4 |