KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 4

Flat surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map

Emel ÇOŞKUN
UĞUR DURSUN
Sayfa
613–629
Yayın Tarihi
2022-11-05
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)

We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
📊
Temel Bulgular & Veri:We also prove that right circular cones and hyperbolic cones in $Bbb{E}_{1}^{3}$ are the only cones in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
💡
Sonuç & Katkı:We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in $Bbb{E}_{1}^{3}$ are the only cones in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.

🔖

Bu Makaleye Atıf Yap

ÇOŞKUN, E., DURSUN, U. (2022). Flat surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 4, 613–629. https://ajindex.com/articles/608413

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (21)

  1. Arslan, K., Bayram, B.K., Bulca, B., Kim, Y.H., Murathan, C., Öztürk, G.: Rotational embeddings in $E^{4}$ with pointwise 1-type Gauss map, Turk. J. Math. 35, 493–499 (2011)
  2. Baikoussis, C., Blair, D.E.:, On the Gauss map of ruled surfaces. Glasgow Math. J. 34, 355–359 (1992)
  3. Baikoussis, C., Chen, B.Y., Verstraelen, L.: Ruled surfaces and tubes with finite type Gauss map. Tokyo J. Math. 16, 341–348 (1993)
  4. Baikoussis, C.: Ruled submanifolds with finite type Gauss map. J. Geom. 49, 42–45 (1994)
  5. Baikoussis, C., Verstralen, L.: The Chen-type of the spiral surfaces. Results in Math. 28, 214–223 (1995)
  6. Chen, B.Y.: Total Mean Curvature and Submanifolds of Finite Type. Singapore-New Jersey-London. World Scientific, 1984
  7. Chen, B.Y.: Null 2-type surfaces E3 are circular cylinder. Kodai Math J. 11, 295–299 (1988)
  8. Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117–337 (1996)
  9. Chen, B.Y., Piccinni, P.: Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35, 161–186 (1987)
  10. Chen, B.Y., Choi, M., Kim, Y.H.: Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. Soc. 42, 447–455 (2005)
  11. Choi, M., Kim, Y.H.: Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38, 753–761 (2001)
  12. Dursun, U.: Null 2-type submanifolds of the Euclidean space E5 with parallel normalized mean curvature vector. Kodai Math. J. 28, 191–198 (2005)
  13. Dursun, U.: Hypersurfaces with pointwise 1-type Gauss map, Taiwanese J. Math. 11, 1407–1416 (2007)
  14. Dursun, U.: Hypersurfaces with pointwise 1-type Gauss map in Lorentz-Minkowski space. Proc. Est. Acad. Sci. 58, 146–161 (2009)
  15. Dursun, U.: Flat surfaces in the Euclidean space E3 with pointwise 1-type Gauss map. Bull. Malays. Math. Sci. Soc. (2) 33, 469–478 (2010)
  16. Ferrandez, A., Lucas, P.: Null finite type hypersurfaces in space forms. Kodai Math. J. 14, 406–419 (1991)
  17. Graves, L.K.: Codimension one isometric immersions between Lorentz Spaces. Trans. Amer. Math.Soc. 252, 367–392 (1979)
  18. Greub, W.H.: Linear Algebra. New York. Springer, 1963
  19. Ki, U.H., Kim, D.S., Kim, Y.H., Roh, Y.M.: Surfaces of revolution with pointwise 1-type Gauss map in Minkowski 3-space. Taiwanese J. Math. 13, 317–338 (2009)
  20. Kim, Y.H., Yoon, D.W.: Ruled surfaces with pointwise 1-type Gauss map. J. Geom. Phys. 34, 191–205 (2000)
  21. Kim, Y.H., Yoon, D.W.: Classification of r