Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2021 / Cilt: 11 - Sayı: 2

On Surfaces in pseudo-Galilean space with prescribed mean curvature

Yarı-Galileo Uzayında Belli Bir Ortalama Eğriliğe Sahip Yüzeyler Üzerine

Pages
215–226
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

We classify these surfaces that satisfy the equation H=v^ , where H is the mean curvature and v^the normal component of an isotropic vector v.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we consider certain classes of surfaces in the pseudo-Galilean space, the translation and factorable surfaces.
📊
Key Findings & Data:In this work, we consider certain classes of surfaces in the pseudo-Galilean space, the translation and factorable surfaces.
💡
Conclusion & Impact:We classify these surfaces that satisfy the equation H=v^ , where H is the mean curvature and v^the normal component of an isotropic vector v.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, we consider certain classes of surfaces in the pseudo-Galilean space, the translation and factorable surfaces. We classify these surfaces that satisfy the equation H=v^ , where H is the mean curvature and v^the normal component of an isotropic vector v.

Özet

Bu çalışmada; yarı-Galileo uzayında, öteleme ve ayrışabilir yüzeyler denilen iki belirgin sınıf ele alınmıştır. 𝑣 , bir 𝑣 izotropik vektörün normal bileşeni olmak üzere bu yüzeylerdenortalama eğriliği 𝐻 = 𝑣! denklemini sağlayanlar elde edilmiştir.

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Cite This Article

AYDIN, M. E., ÖĞRENMİŞ, A. O. (2022). On Surfaces in pseudo-Galilean space with prescribed mean curvature. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 11 - Sayı: 2, 215–226. https://ajindex.com/articles/428022

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References (17)

  1. Bueno, A., Translating solitons of the mean curvature flow in the space H^2×R, Journal of Geometry, (109, Article number )42, 2018. https://doi.org/10.1007/s00022-018-0447-x, 2018
  2. López, R., Separation of variables in equations of mean-curvature type, Proceedings of the Royal Society of Edinburgh Section A, (146)5146(5), 1017-1035, 2016
  3. López, R., Some geometric properties of translating solitons in Euclidean space, Journal of Geometry, (109, Article number )40, 2018.
  4. Aydin, M.E., López, R., Ruled translating solitons in Minkowski 3-space, preprintarXiv:2109.05254v1, 2021
  5. Aydin, M.E., López, R., Translating solitons by separation of variables, arXiv:2109.05253v1 preprint, 2021
  6. Angenent, S., On the formation of singularities in the curve shortening flow, Journal of Differential Geometry, 33, 601-633, 1991
  7. Halldorsson, H., Self-similar solutions to the curve shortening flow, Transactions of the American Mathematical Society, (364)10364(10), 5285-5309, 2012
  8. Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers, Open Mathematics, 16,747-766, 2018
  9. Altiin, M., Kazan, A., Karadag, H. B., Ruled surfaces in E^3 with density, Honam Mathematical Journal,. 41(4), 683-695, 2019
  10. Hieu, D.T., Hoang, N.M., Ruled minimal surfaces in R^3 with density e^z, Pacific Journal of Mathematics, (243)2243(2), 277-285, 2009
  11. Abdel-Aziz, H.S., Saad, M.K., Ali, H.A., Affine factorable surfaces in pseudo-Galilean space, arXiv:1812.00765v1 [math.GM]
  12. Aydin, M. E.,, Ogrenmis, A.O., Ergut, M., Classification of factorable surfaces in the pseudo-Galilean space, Glasnik Matematicki Series III, (70)5050(70), 441-451, 2015
  13. Aydin, M. E., Kulahci, M. A., Ogrenmis, A.O., Non-zero constant curvature factorable surfaces in pseudo-Galilean space, Communications of the Korean Mathematical Society, 33 (1), 247-259, 2018
  14. Aydin, M. E., Kulahci, M. A., Ogrenmis, A.O., Constant curvature translation surfaces in Galilean 3-space, International Electronic Journal of Geometry, 12(1), 9-19, 2019
  15. Dede, M., Ekici, C., On minimal surfaces in Galilean space, Conference Proceedings of Science and Technology, (2)22(2), 142-147, 2019
  16. Kelleci, A.,, Translation-factorable surfaces with vanishing curvatures in Galilean 3-spaces, International Journal of Maps in Mathematics, (4)14(1), 14-26, 2021
  17. Milin-Sipus, Z.,