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Dergiler / 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
Sayfa
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Yayın Tarihi
2024-06-21
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study minimal translations surfaces in a strict Walker 3-manifold.
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Temel Bulgular & Veri:Based on the existence of two isometries, we classify minimal translation surfaces on this class of manifold.
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Sonuç & Katkı:Some drawings have been added to illustrate the shape of certain surfaces.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (15)

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  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.
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  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