Öz
In this paper, by using a hyperbolic lifting transformation to a plane curve,
we construct an envelope ruled surface. Then we show that it is a developable
surface in three dimensional Euclidean space and we give the conditions of this
surface to be a minimal surface and constant mean curvature surface. Finally,
we constructed some examples and graph the curves and surfaces given in examples. In this paper, by using a hyperbolic lifting transformation to a plane curve, we construct an envelope ruled surface. Then we show that it is a developable surface in three dimensional Euclidean space and we give the conditions of this surface to be a minimal surface and constant mean curvature surface. Finally, we constructed some examples and graph the curves and surfaces given in examples.
Anahtar Kelimeler
Ruled surface Developable surface Envelope surface Curve lifting
Kaynakça
- [1] Ali AT, Aziz HS, Sorour AH, 2013. Ruled surfaces generated by some special curves in Euclidean 3-space, J. of the Egyp. Math. Soc., 21: 285-294.
- [2] Choi JJ, Kim MS, Elber G, 1997. Computing Planar Bisector Curves Based on Developable SSI, Preprint, POSTECH, Korea.
- [3] Çöken AC, Çiftci Ü, Ekici C, 2008. On parallel timelike ruled surfaces with timelike rulings, Kuwait Journal of Science & Engineering, 35(1): 21-31.
- [4] Do Carmo MP, 1976. Di¤erential geometry of curves and surfaces, Prentice Hall, Englewood Cli¤s, NJ.
- [5] Gray A, 1993. Modern di¤erential geometry of curves and surfaces with mathematica, 2nd Ed., Boca Raton, FL: Crc Press.
- [6] Izumiya S, Takeuchi N, 2004. New special curves and developable surfaces, Turk. J. Math., 28: 153-163.
- [7] Izumiya S, Takeuchi N, 2003. Special curves and ruled surfaces, Contributions to Algebra and Geometry, 44(1): 203-212.
- [8] Kühnel W, 1994. Ruled W-surfaces, Arch. Math., 62: 475-480.
- [9] Kühnel W, 2006. Di¤erential geometry of curves-surfaces-manifolds, Second Ed. AMS, Providence.
- [10] Osserman R, 1986. A survey of minimal surfaces, Dover Publications Inc., Mineola, New York.
- [11] Ravani B, Ku TS, 1991. Bertrand O¤sets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2): 145-152.
- [12] Yu Y, Liu H, Jung SD, 2014. Structure and characterization of ruled surfaces in Euclidean 3-space, Applied Math. and Comp., 233: 252-259.
Öz
Bu makalede, bir düzlemsel eğriye hiperbolik yükseltme dönüşümü uygulayarak, regle zarf yüzeyi inşa ettik. Daha sonra bu yüzeyin üç boyutlu Öklid uzayında açılabilir yüzey olduğunu gösterdik ve bu yüzeyin minimal yüzey ve sabit ortalama eğrilikli yüzey olabilmesi için koşulları verdik. Son olarak, bazı örnekler verdik ve örneklerdeki eğrilerin ve yüzeylerin grafiklerini çizdik. Bu makalede, bir düzlemsel eğriye hiperbolik yükseltme dönüşümü uygulayarak, regle zarf yüzeyi inşa ettik. Daha sonra bu yüzeyin üç boyutlu Öklid uzayında açılabilir yüzey olduğunu gösterdik ve bu yüzeyin minimal yüzey ve sabit ortalama eğrilikli yüzey olabilmesi için koşulları verdik. Son olarak, bazı örnekler verdik ve örneklerdeki eğrilerin ve yüzeylerin grafiklerini çizdik.
Anahtar Kelimeler
Kaynakça
- [1] Ali AT, Aziz HS, Sorour AH, 2013. Ruled surfaces generated by some special curves in Euclidean 3-space, J. of the Egyp. Math. Soc., 21: 285-294.
- [2] Choi JJ, Kim MS, Elber G, 1997. Computing Planar Bisector Curves Based on Developable SSI, Preprint, POSTECH, Korea.
- [3] Çöken AC, Çiftci Ü, Ekici C, 2008. On parallel timelike ruled surfaces with timelike rulings, Kuwait Journal of Science & Engineering, 35(1): 21-31.
- [4] Do Carmo MP, 1976. Di¤erential geometry of curves and surfaces, Prentice Hall, Englewood Cli¤s, NJ.
- [5] Gray A, 1993. Modern di¤erential geometry of curves and surfaces with mathematica, 2nd Ed., Boca Raton, FL: Crc Press.
- [6] Izumiya S, Takeuchi N, 2004. New special curves and developable surfaces, Turk. J. Math., 28: 153-163.
- [7] Izumiya S, Takeuchi N, 2003. Special curves and ruled surfaces, Contributions to Algebra and Geometry, 44(1): 203-212.
- [8] Kühnel W, 1994. Ruled W-surfaces, Arch. Math., 62: 475-480.
- [9] Kühnel W, 2006. Di¤erential geometry of curves-surfaces-manifolds, Second Ed. AMS, Providence.
- [10] Osserman R, 1986. A survey of minimal surfaces, Dover Publications Inc., Mineola, New York.
- [11] Ravani B, Ku TS, 1991. Bertrand O¤sets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2): 145-152.
- [12] Yu Y, Liu H, Jung SD, 2014. Structure and characterization of ruled surfaces in Euclidean 3-space, Applied Math. and Comp., 233: 252-259.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Ağustos 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 13 Sayı: 2 |