Research Article
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Year 2023, , 328 - 335, 30.06.2023
https://doi.org/10.17776/csj.1197746

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

Year 2023, , 328 - 335, 30.06.2023
https://doi.org/10.17776/csj.1197746

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.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Yunus Öztemir 0000-0001-8292-1986

Mustafa Çalışkan 0000-0003-0342-571X

Publication Date June 30, 2023
Submission Date November 1, 2022
Acceptance Date April 7, 2023
Published in Issue Year 2023

Cite

APA Öztemir, Y., & Çalışkan, M. (2023). The Intersection of Two Ruled Surfaces Corresponding to Spherical Indicatrix Curves on the Unit Dual Sphere. Cumhuriyet Science Journal, 44(2), 328-335. https://doi.org/10.17776/csj.1197746