KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

A new approach to revolution surface with its focal surface in the Galilean 3-space $\mathbb{G}_{3}$

İlim Kişi
Sayfa
1722–1737
Yayın Tarihi
2022-10-18
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)

Also, by giving some examples to these surfaces, we present the visualizations of each type of focal surface of surface of revolution in $\mathbb{G}_{3}$.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we handle focal surfaces of surface of revolution in Galilean 3-space $\mathbb{G}_{3}$.
📊
Temel Bulgular & Veri:We define the focal surfaces of surface of revolution and we obtain some results for these types of surfaces to become flat and minimal.
💡
Sonuç & Katkı:Also, by giving some examples to these surfaces, we present the visualizations of each type of focal surface of surface of revolution in $\mathbb{G}_{3}$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:line congruence · focal surface · surface of revolution

Abstract

In this paper, we handle focal surfaces of surface of revolution in Galilean 3-space $\mathbb{G}_{3}$. We define the focal surfaces of surface of revolution and we obtain some results for these types of surfaces to become flat and minimal. Also, by giving some examples to these surfaces, we present the visualizations of each type of focal surface of surface of revolution in $\mathbb{G}_{3}$.

🔖

Bu Makaleye Atıf Yap

Kişi, İ. (2022). A new approach to revolution surface with its focal surface in the Galilean 3-space $\mathbb{G}_{3}$. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1722–1737. https://ajindex.com/articles/529983

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (18)

  1. D. Aberre and K. Agraval, Surfaces of revolution in n dimensions, Int. J. Math. Educ. Sci. Technol. 38, 843-852, 2009
  2. K. Arslan, B. Kılıç Bayram, B. Bulca and G. Öztürk, Generalized rotation surfaces in $\mathbb{E}^4$, Results. Math. 61, 315-327, 2012
  3. K. Arslan, B. Bayram, B. Bulca, D. Kosova and G. Öztürk, Rotational surfaces in higher dimensional Euclidean spaces, Rend. Circ. Mat. Palermo (2) 67, 59-66, 2018
  4. M.E. Aydın, M.A. Külahçı and A.O. Öğrenmiş, Constant curvature translation surfaces in Galilean 3-space, Int. Electron. J. Geom. 12, 9-19, 2019
  5. D.V. Cuong, Surfaces of revolution with constant Gaussian curvature in four-space, Asian-Eur. J. Math. 6, 1350021-1–1350021-7, 2013
  6. M. Dede, C. Ekici and A.C. Çöken, On the parallel surfaces in the Galilean space, Hacet. J. Math. Stat. 42, 605-615, 2013
  7. M. Dede, C. Ekici and W. Goemans, Surfaces of revolution with vanishing curvature in Galilean 3-space, Zh. Mat. Fiz. Anal. Geom. 14, 141-152, 2018
  8. W. Goemans, Flat double rotational surfaces in Euclidean and Lorentz-Minkowski 4-space, Publ. Inst. Math. 103, 61-68, 2018
  9. A. Gray, E. Abbana and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, (3rd edition), Studies in Advanced Mathematics, Chapman and Hall/CRC, Boca Raton, FL, 2006
  10. H. Hagen and S. Hahmann, Generalized Focal Surfaces: A New Method for Surface Interrogation, Proceedings Visualization’92, Boston, 70-76, 1992
  11. H. Hagen, H. Pottmann and A. Divivier, Visualization functions on a surface, J. Visual. Comput. Anim. 2, 52-58, 1991
  12. A. Kazan and H. Karadağ, A classification of surfaces of revolution in Lorentz- Minkowski space, Int. J. Contemp. Math. Sci. 6, 1915-1928, 2011
  13. K. Kenmotsu, Surfaces of revolution with prescribed mean curvature, Tohoku Math. J. 32, 147-153, 1980
  14. K. Kenmotsu, Surfaces of revolution with periodic mean curvature, Osaka J. Math. 40, 687-696, 2003
  15. B. Özdemir, A characterization of focal curves and focal surfaces in $\mathbb{E}^4$, Ph.D. Thesis, Uludağ University, 2008
  16. B. Özdemir and K. Arslan, On generalized focal surfaces in $\mathbb{E}^3$, Rev. Bull. Calcutta Math. Soc. 16, 23-32, 2008
  17. G. Öztürk and K. Arslan, On focal curves in Euclidean n-space $\mathbb{R}^n$, Novi Sad J. Math. 48, 35-44, 2016
  18. B.J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space $\mathbb{G}^3$, Glas. Mat. Ser. III 22, 449-457, 1987