Abstract
In this study, using Darboux frame {T,g,n} of ruled surface ϕ(s,v), the evolute offsets ϕ^{∗}(s,v) with Darboux frame {T^{∗},g^{∗},n^{∗}} of ϕ(s,v) are defined. Characteristic properties of ϕ^{∗}(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces ϕ_{T^{∗}}^{∗},ϕ_{g^{∗}}^{∗} and ϕ_{n^{∗}}^{∗} are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfaffian vectors of motions H/H′ and H^{∗}/H^{∗′}, where H={T,g,n} be the moving space along the base curve of ϕ(s,v), H^{∗}={T^{∗},g^{∗},n^{∗}} be the moving space along the base curve of ϕ^{∗}(s,v), H′ and H^{∗′} be fixed Euclidean spaces.
Keywords
References
- Boyer, C.A. History of mathematics, New-York, Wiley, 1968.
- Ravani, B. and Ku, T.S. Bertrand offsets of ruled and developable surfaces, Comp Aided Geom Design, 23 (2), (1991), 145--152.
- Kasap, E. and Kuruoğlu, N. The Bertrand offsets of ruled surfaces in R₁³, Acta Math. Vietnam, 31 (1), (2006), 39--48.
- Kasap, E. and Yüce, S. and Kuruoğlu, N. The Involute-Evolute Offsets of Ruled Surfaces, Iran. J. Sci. Technol. A, (2009), 32 (A2), 195--201.
- Orbay, K. and Kasap,E. and Aydemir, İ. Mannheim offsets of ruled surfaces. Math Problems Engineering, (2009), Article Id 160917.
- Yoon, D.W. On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish Journal of Mathematics, 40, (2016), 594--604.
- Şentürk, G.Y. and Yüce, S. Characteristic properties of the ruled surface with Darboux Frame in E³, Kuwait J Sci, 42 (2), (2015) 14--33.
- Şentürk, G.Y. and Yüce, S. Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), (2017) 1151-1159.
- Bektaş, Ö. and Yüce, S. Special involute-evolute partner D-curves in E³, European Journal of Pure and Applied Mathematics, (2013) 6(1), 20--29.
- Darboux, G. Leçons sur la Thèorie gènèrale des Sufaces I-II-III-IV, Gauthier- Villars, Paris, 1896.
Abstract
References
- Boyer, C.A. History of mathematics, New-York, Wiley, 1968.
- Ravani, B. and Ku, T.S. Bertrand offsets of ruled and developable surfaces, Comp Aided Geom Design, 23 (2), (1991), 145--152.
- Kasap, E. and Kuruoğlu, N. The Bertrand offsets of ruled surfaces in R₁³, Acta Math. Vietnam, 31 (1), (2006), 39--48.
- Kasap, E. and Yüce, S. and Kuruoğlu, N. The Involute-Evolute Offsets of Ruled Surfaces, Iran. J. Sci. Technol. A, (2009), 32 (A2), 195--201.
- Orbay, K. and Kasap,E. and Aydemir, İ. Mannheim offsets of ruled surfaces. Math Problems Engineering, (2009), Article Id 160917.
- Yoon, D.W. On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish Journal of Mathematics, 40, (2016), 594--604.
- Şentürk, G.Y. and Yüce, S. Characteristic properties of the ruled surface with Darboux Frame in E³, Kuwait J Sci, 42 (2), (2015) 14--33.
- Şentürk, G.Y. and Yüce, S. Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), (2017) 1151-1159.
- Bektaş, Ö. and Yüce, S. Special involute-evolute partner D-curves in E³, European Journal of Pure and Applied Mathematics, (2013) 6(1), 20--29.
- Darboux, G. Leçons sur la Thèorie gènèrale des Sufaces I-II-III-IV, Gauthier- Villars, Paris, 1896.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | August 1, 2019 |
| Submission Date | October 19, 2017 |
| Acceptance Date | January 8, 2019 |
| Published in Issue | Year 2019 Volume: 68 Issue: 2 |
Cite
Cited By
Smarandache Ruled Surfaces according to Darboux Frame in E 3
Journal of Mathematics
https://doi.org/10.1155/2021/9912624
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
