Dergiler / Communication in Mathematical Modeling and Applications / 2026 / Cilt: 1 Sayı: 1

Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space

Sayfa
26–43
Yayın Tarihi
2016-01-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

By using this rotation vector, we compute pitch length and pitch angle of the parallel ruled surfaces with Darboux frame. 

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, the parallel ruled surfaces with Darboux frame are introduced in Euclidean 3-space.
📊
Temel Bulgular & Veri:Then some characteristic properties such as developability, striction point and distribution parameter of the parallel ruled surfaces with Darboux frame are given in Euclidean 3-space.
💡
Sonuç & Katkı:By using this rotation vector, we compute pitch length and pitch angle of the parallel ruled surfaces with Darboux frame. 
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Parallel ruled surface · Darboux frame · developability

Abstract

In this paper, the parallel ruled surfaces with Darboux frame are introduced in Euclidean 3-space. Then some characteristic properties such as developability, striction point and distribution parameter of the parallel ruled surfaces with Darboux frame are given in Euclidean 3-space. Then we obtain Steiner rotation vector of this kind of surfaces Euclidean 3-space. By using this rotation vector, we compute pitch length and pitch angle of the parallel ruled surfaces with Darboux frame. 

🔖

Bu Makaleye Atıf Yap

Unluturk, Y., Cimdiker, M., Ekici, C. (2016). Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. Communication in Mathematical Modeling and Applications, Cilt: 1 Sayı: 1, 26–43. https://ajindex.com/articles/1648696

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. Aydemir, I. & Kasap, E. 2005. Timelike ruled surface with spacelike rulings in R. Kuwait Journal of Science & Engineering 32(2): 13-24.
  2. C¸ oken, A.C., C¸ iftc¸i, ¨ U. & Ekici, C. 2008. On parallel timelike ruled surfaces with timelike rulings. Kuwait Journal of Science & Engineering 35(1): 21-31.
  3. Darboux, G. 1896. Lec¸ons sur la theorie generale des surfaces I-II-III-IV., Gauthier-Villars, Paris.
  4. Gray, A., Salamon, S. & Abbena, E. 2006. Modern differential geometry of curves and surfaces with Mathematica. Chapman and Hall/CRC.
  5. Hacısalihoglu, H. H. 1983. Diferensiyel geometri. Inonu Univ. Fen Edebiyat Fak. Yay. No.2.
  6. Hlavaty, V. 1945. Differentielle linien geometrie. Uitg P. Noorfhoff, Groningen.
  7. Hoschek, J. 1973. Integral invarianten von regelflachen. Arch. Math, XXIV.
  8. Karadag, H. B., Kılıc¸, E. & Karadag, M. 2014. On the developable ruled surfaces kinematically generated in Minkowski 3-Space. Kuwait Journal of Science 41(1): 21-34.
  9. Kuhnel, W. 2002. Differential geometry, curves-surfaces-manifolds. American Mathematical Society. ¨
  10. Muller, H. R. 1978. Verallgemeinerung einer formelvon Steiner. Abh. Braunschweig Wiss. Ges. 31:107-113, 1978.
  11. O’Neill, B. 1996. Elementary differential geometry. Academic Press Inc, New York.
  12. Ravani, T. & Ku S. 1991. Bertrand offsets of ruled surface and developable surface. Comp Aided Geom Design 23(2):145-152.
  13. Savcı, Z. 2011. On parallel ruled Weingarten surfaces in 3-dimensional Euclidean space. (in Turkish) PhD Thesis, Eskisehir Osmangazi Univ. Grad. Sch. Nat. Sci., Eskisehir.
  14. Senturk, G. Y. & Y ¨ uce, S. 2015. Characteristic properties of the ruled surface with Darboux frame in E3. Kuwait Journal of Science, 42(2):14-33.
  15. Senturk, G. Y. & Y ¨ uce, S. 2015a. Properties of integral invariants of the involute-evolute offsets of ruled surfaces. Int. J. Pure Appl. Math. 102(4):757-768.
  16. Unluturk, Y. & Ekici, C. 2014. Parallel surfaces satisying the properties of ruled surfaces in Minkowski 3-space. Global Journal of Science Frontier Research F, 14(1):78-95.