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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 2

Minimals translation surfaces in a strict Walker 3-manifold

Athoumane Nıang(Université Cheikh Anta Diop)0000-0003-4390-6438
Ameth Ndiaye(Université Cheikh Anta Diop)0000-0003-0055-1948
Abdoul Salam Diallo(Université Alioune Diop de Bambey)0000-0003-4254-5829
Pages
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Publication Date
2024-06-21
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AI Summary & Key Takeaways

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

Some drawings have been added to illustrate the shape of certain surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study minimal translations surfaces in a strict Walker 3-manifold.
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Key Findings & Data:Based on the existence of two isometries, we classify minimal translation surfaces on this class of manifold.
💡
Conclusion & Impact:Some drawings have been added to illustrate the shape of certain surfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Minimal surfaces · translation surfaces · Walker manifolds

Abstract

In this paper, we study minimal translations surfaces in a strict Walker 3-manifold. Based on the existence of two isometries, we classify minimal translation surfaces on this class of manifold. Some drawings have been added to illustrate the shape of certain surfaces.

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Cite This Article

Nıang, A., Ndiaye, A., Diallo, A. S. (2024). Minimals translation surfaces in a strict Walker 3-manifold. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 2. https://doi.org/10.31801/cfsuasmas.1296991

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References (15)

  1. Brozos-Vazquez, M., Garcia-Rio, E., Gilkey, P., Nikevic, S., Vazquez-Lorenzo, R., The Geometry of Walker Manifolds, Synthesis Lectures on Mathematics and Statistics, 5. Morgan and Claypool Publishers, Williston, VT, 2009.
  2. Calvaruso, G., Van der Veken, J. Parallel surfaces in Lorentzian three-manifolds admitting a parallel null vector field, J. Phys. A: Math. Theor., 43 (2010) 325207, 9 pp. https://doi.org/10.1088/1751-8113/43/32/325207
  3. Darboux, G. Lessons on the General Theory of Surfaces. I, II, Editions Jacques Gabay, Sceaux, 1993. 604 pp.
  4. Diallo, A. S., Ndiaye, A., Niang, A., Minimal Graphs on Three-Dimensional Walker Manifolds, Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, 425-438, Trends Math., Birkhauser/Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-57336-2-17
  5. Dillen, F., Verstraele, L., Zafindratafa, G., A Generalization of the Translation Surfaces of Scherk, In: Differential Geometry in Honor of Radu Rosca. K. U. L., (1991), 107-109.
  6. Inoguchi, I., Lopez, R., Munteanu, M. I., Minimal translation surfaces in the Heisenberg group Nil3, Geom. Dedicata, 16 (2012), 221-231. https://doi.org/10.1007/s10711-012-9702-8
  7. Liu, H., Yu, Y., Affine translation surfaces in Euclidean 3-space, Proc. Japan Acad. Ser. A, 89 (2013), (9), 111-113. https://doi.org/10.3792/pjaa.89.111
  8. Lopez, R., Minimal translation surfaces in hyperbolic space, Beitrage Alge. Geom., 52 (2011), 105-112. https://doi.org/10.1007/s13366-011-0008-z
  9. Moruz, M., Munteanu, M. I., Minimal translation hypersurfaces in E4, J. Math. Analysis Appl., 439 (2016), 798-812. https://doi.org/10.1016/j.jmaa.2016.02.077
  10. Niang, A., Ndiaye, A., Diallo, A. S., A Classification of Strict Walker 3-Manifold, Konuralp J. Math., 9(1) (2021), 148-153.
  11. Scherk, H. F., Bemerkungen uber die kleinste Flache innerhalb gegebener Grenzen, J. Reine Angew. Math., 13 (1835), 185-208.
  12. Yang, D., Fu, Y., On affine translation surfaces in affine space, J. Math. Analysis Appl., 440 (2016) 437-450. https://doi.org/10.1016/j.jmaa.2016.03.066
  13. Yoon, D. W., Lee, C. W., Karacan, M. K., Some translation surfaces in the 3- dimensional Heisenberg group, Bull. Korean Math. Soc., 50(4) (2013), 1329-1343. https://doi.org/10.4134/BKMS.2013.50.4.1329
  14. Yoon, D. W., Weighted minimal translation surfaces in the Galilean space with density, Open Math., 15 (1) (2017), 459-466. https://doi.org/10.1515/math-2017-0043
  15. Walker, A. G., Canonical form for a Riemannian space with a parallel field of null planes, Quart. J. Math., Oxford, 1(1) (1950), 69-79. https://doi.org/10.1093/qmath/1.1.69