Abstract
References
- [1] Carmo M. Do., Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, (1976) 1-114.
- [2] Karaca E., Çalışkan M., Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves, Gazi Univ. J. Sci., 33(5) (2020) 751-759.
- [3] Altınkaya A., Çalışkan M., On the Curvatures of the Ruled Surfaces of b-Lift Curves, Cumhuriyet Sci. J., 42(4) (2021) 873-877.
- [4] Izumiya S., Takeuchi N., New Special Curves and Developable Surfaces, Turk. J. Math., 28(2) (2004) 153-163.
- [5] Uyar Düldül B., Çalışkan M., On the Geodesic Torsion of a Tangential Intersection Curve of Two Surfaces in R^3, Acta Math. Univ. Comen., 82(2) (2013) 177-189.
- [6] Ye X., Maekawa T., Differential Geometry of Intersection Curves of Two Surfaces, Comput. Aided Geom. Des., 16(8) (1999) 767-788.
- [7] Heo H-S., Kim M-S., Elber G., The Intersection of Two Ruled Surfaces, Comput. Aided Des., 31(1) (1999) 33-50.
- [8] Fischer I.S., Dual-Number Methods in Kinematics, Statics and Dynamics. Boca Raton, London, New York, Washington DC: CRC Press, (1999).
- [9] Yaylı Y., Saraçoğlu S., Different Approaches to Ruled Surfaces, SDU J. Sci., 7(1) (2012) 56-68.
- [10] Karaca E., Çalışkan M., Dual Spherical Curves of Natural Lift Curve and Tangent Bundles of Unit 2-Sphere, J. Sci.and Arts, 3(48) (2019) 561-574.
- [11] Arslan Güven İ., Kaya Nurhan S., Karacan M-K., Ruled Weingarten Surfaces Related to Dual Spherical Curves, Gen. Math. Not., 24(2) (2014) 10-17.
The Intersection of Two Ruled Surfaces Corresponding to Spherical Indicatrix Curves on the Unit Dual Sphere
Abstract
In this study, we first investigate the intersection of two different ruled surfaces in R^3 for two different tangential spherical indicatrix curves on DS^2 using the E. Study mapping. The conditions for the intersection of these ruled surfaces in R^3 are expressed by theorems with bivariate functions. Secondly, considering two different principal normal spherical indicatrix curves on DS^2, we examine the intersection of two different ruled surfaces in R^3 by using E. Study mapping. Similarly, the conditions for the intersection of these ruled surfaces in R^3 are indicated by theorems with bivariate functions. Thirdly, using E. Study mapping, we explore the intersection of two different ruled surfaces in R^3 by considering two different binormal spherical indicatrix curves on DS^2. Likewise, the conditions for the intersection of these ruled surfaces in R^3 are denoted by theorems with bivariate functions. Fourthly, considering two different pole spherical indicatrix curves on DS^2, we study the intersection of two different ruled surfaces in R^3 by using E. Study mapping. In the same way, the conditions for the intersection of these ruled surfaces in R^3 are specified by theorems with bivariate functions. Finally, we provide some examples that support the main results.
References
- [1] Carmo M. Do., Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, (1976) 1-114.
- [2] Karaca E., Çalışkan M., Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves, Gazi Univ. J. Sci., 33(5) (2020) 751-759.
- [3] Altınkaya A., Çalışkan M., On the Curvatures of the Ruled Surfaces of b-Lift Curves, Cumhuriyet Sci. J., 42(4) (2021) 873-877.
- [4] Izumiya S., Takeuchi N., New Special Curves and Developable Surfaces, Turk. J. Math., 28(2) (2004) 153-163.
- [5] Uyar Düldül B., Çalışkan M., On the Geodesic Torsion of a Tangential Intersection Curve of Two Surfaces in R^3, Acta Math. Univ. Comen., 82(2) (2013) 177-189.
- [6] Ye X., Maekawa T., Differential Geometry of Intersection Curves of Two Surfaces, Comput. Aided Geom. Des., 16(8) (1999) 767-788.
- [7] Heo H-S., Kim M-S., Elber G., The Intersection of Two Ruled Surfaces, Comput. Aided Des., 31(1) (1999) 33-50.
- [8] Fischer I.S., Dual-Number Methods in Kinematics, Statics and Dynamics. Boca Raton, London, New York, Washington DC: CRC Press, (1999).
- [9] Yaylı Y., Saraçoğlu S., Different Approaches to Ruled Surfaces, SDU J. Sci., 7(1) (2012) 56-68.
- [10] Karaca E., Çalışkan M., Dual Spherical Curves of Natural Lift Curve and Tangent Bundles of Unit 2-Sphere, J. Sci.and Arts, 3(48) (2019) 561-574.
- [11] Arslan Güven İ., Kaya Nurhan S., Karacan M-K., Ruled Weingarten Surfaces Related to Dual Spherical Curves, Gen. Math. Not., 24(2) (2014) 10-17.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2023 |
| Submission Date | November 1, 2022 |
| Acceptance Date | April 7, 2023 |
| Published in Issue | Year 2023 |