SavedAdd your journal

Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2020 / Cilt: 13 - Sayı: ÖZEL SAYI I

Surfaces Constructed by Non-Null Planar Curves with Vanishing Weighted Curvature in 𝑬𝟏𝟑 with Density 𝒆𝒂𝒙+𝒃𝒚

e^(ax+by) Yoğunluklu E^3_1 Uzayında Sıfır Ağırlıklı Eğriliğe Sahip Null Olmayan Düzlemsel Eğrilerin Oluşturduğu Yüzeyler

Mustafa ALTIN
Ahmet KAZAN
H.bayram KARADAĞ
Pages
45–55
Publication Date
2020-02-28
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.
📊
Key Findings & Data:In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.
💡
Conclusion & Impact:In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ağırlıklı eğrilik · yoğunluklu Lorentz-Minkowski uzayı · spacelike eğri

Abstract

In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.

Özet

Bu çalışmada, e^(ax+by) yoğunluklu E^3_1 Lorentz-Minkowski uzayında, ikisi aynı anda sıfır olmayan a ve b sabitlerinin durumlarına göre, ağırlıklı eğrilikleri sıfır olan spacelike ve timelike düzlemsel eğriler yardımıyla oluşturulan dönel yüzeyler ve regle yüzeyler çalışılmıştır.

🔖

Cite This Article

ALTIN, M., KAZAN, A., KARADAĞ, H. (2020). Surfaces Constructed by Non-Null Planar Curves with Vanishing Weighted Curvature in 𝑬𝟏𝟑 with Density 𝒆𝒂𝒙+𝒃𝒚. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 - Sayı: ÖZEL SAYI I, 45–55. https://ajindex.com/articles/233917

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. Abdel-Aziz, H.S. and Saad, M.K., 2015, “Smarandache Curves of Some Special Curves in the Galilean 3-Space”, Honam Mathematical Journal, 37(2), 253-264
  2. Albujer, A.L. and Caballero, M., 2017, “Geometric Properties of Surfaces with the Same Mean Curvature in R^3 and L^3”, J. Math. Anal. Appl., 445, 1013-1024
  3. Ali, A.T., 2010, “Special Smarandache Curves in the Euclidean Space”, Int. J. Math. Comb., 2, 30-36
  4. Ali, A.T., 2012, “Position Vectors of curves in the Galilean Space G_3”, Matematnykn Bechnk, 64(3), 200–210
  5. Baikoussis, C. and Blair, D.E., 1992, “On the Gauss map of ruled surfaces”, Glasgow Math. J., 34, 355-359
  6. Belarbi, L. and Belkhelfa, M., 2012, “Surfaces in R^3 with Density”, i-manager’s Journal on Mathematics, 1(1), 34-48
  7. Choi, J.H., Kim, Y.H. and Ali, A.T., 2012, “Some associated curves of Frenet non-lightlike curves in E_1^3”, J. Math. Anal. Appl., 394, 712–723
  8. Corwin, I., Hoffman, N., Hurder, S., Sesum, V. and Xu, Y., 2006, “Differential geometry of manifolds with density”, Rose-Hulman Und. Math. J., 7(1), 1-15
  9. Dillen, F., Pas, J. and Verstraelen, L., “On the Gauss map of surfaces of revolution”, Bull. Inst. Math. Acad. Sinica, 18, 239-246
  10. Dillen, F. and Kühnel, W., 1999, “Ruled Weingarten surfaces in Minkowski 3-space”, Manuscripta Math., 98, 307–320
  11. Divjak, B., 1998, “Curves in Pseudo-Galilean Geometry”, Annales Univ. Sci. Budapest., 41, 117-128
  12. Ekici, C. and Öztürk, H., 2013, “On Time-Like Ruled Surfaces in Minkowski 3-Space”, Universal Journal of Applied Science, 1(2), 56-63
  13. Gromov, M., 2003, “Isoperimetry of waists and concentration of maps”, Geom. Func. Anal., 13, 178-215
  14. Hieu, D.T. and Nam, T.L., 2013, “The classification of constant weighted curvature curves in the plane with a log-linear density”, Commun. Pure Appl. Anal., 13, 1641-1652
  15. Kazan, A. and Karadağ, H.B., 2011, “A Classification of Surfaces of Revolution in Lorentz-Minkowski Space”, Int. J. Contemp. Math. Sciences, Vol. 6, no. 39, 1915-1928
  16. Kazan, A. and Karadağ, H.B., 2018, “Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density”, Int. J. Anal. Appl., 16(3), 414-426
  17. López, R., 2014, “Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space”, Int. Electron. J. Geom., 1, 44–107
  18. Morgan, F., 2005, “Manifolds with Density”, Not. Amer. Math. Soc., 52(8),853-858
  19. Morgan, F., 2006, “Myers’ Theorem With Density”, Kodai Math. J., 29, 4