Journals / Konuralp Journal of Mathematics / 2026 / Volume: 9 Issue: 1

A Classification of Strict Walker 3-Manifold

Athoumane Nıang(Université Cheikh Anta Diop)
Ameth Ndiaye(Université Cheikh Anta Diop)
Abdoul Salam Diallo(Université Alioune Diop de Bambey)
Pages
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Publication Date
2021-04-28
DOI
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AI Summary & Key Takeaways

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

The local degeneracy (resp. non-degeneracy) of one of this family has a strong consequence on the geometry of the ambiant Walker manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we give two special families of ruled surfaces in a three dimensional strict Walker manifold.
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Key Findings & Data:In this paper we give two special families of ruled surfaces in a three dimensional strict Walker manifold.
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Conclusion & Impact:The local degeneracy (resp. non-degeneracy) of one of this family has a strong consequence on the geometry of the ambiant Walker manifold.
🔬Design:Review
📍Scope:Comprehensive Sample
⚙️Variables:Minimal surfaces · Lorentz Manifold · Ruled surfaces

Abstract

In this paper we give two special families of ruled surfaces in a three dimensional strict Walker manifold. The local degeneracy (resp. non-degeneracy) of one of this family has a strong consequence on the geometry of the ambiant Walker manifold.

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Cite This Article

Nıang, A., Ndiaye, A., Diallo, A. S. (2021). A Classification of Strict Walker 3-Manifold. Konuralp Journal of Mathematics, Volume: 9 Issue: 1. https://ajindex.com/articles/1521633

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References (11)

  1. M. Brozos-Vàzquez, E. Garca-Rio, P. Gilkey, S. Nikevic and R. Vazquez-Lorenzo. The Geometry of Walker Manifolds, Synthesis Lectures on Mathematics and Statistics, 5. Morgan and Claypool Publishers, Williston, VT, 2009.
  2. M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976. viii+503 pp. 190-191.
  3. M. Chaichi, E. Garcia-Rio and M.E. Vàzquez-Abal, Three-dimensional Lorentz manifolds admitting a parallel null vector eld, J. Phys. A: Math. Gen. 38 (2005), 841-50.
  4. A. S. Diallo and F. Massamba, Some properties of four-dimensional Walker manifolds, New Trends Math. Sci, 5 (2017), (3), 253-261.
  5. A. S. Diallo, A. Ndiaye and A. Niang, Minimal graphs on three-dimensional Walker manifolds, To appear.
  6. G. Calvaruso and J. Van der Veken, Parallel surfaces in Lorentzian three-manifolds admitting a parallel null vector field, J. Phys. A: Math. Theor. 43 (2010) 325-207.
  7. A. Niang, Surfaces minimales réglées dans l'espace de Minkowski ou Euclidien orienté de dimension 3, Afrika Mat. 15 (2003), (3), 117-127.
  8. K. Nomizu and T. Sasaki, Affne Differential Geometry. Geometry of Affne Immersions. Cambridge Tracts in Mathematics Vol. 111 (Cambridge University Press, Cambridge, (1994).
  9. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, (1983).
  10. A. G. Walker, Canonical form for a Riemannian space with a parallel fi eld of null planes, Quart. J. Math. Oxford 1 (1950), (2), 69-79.
  11. I. Van de Woerstyne, Minimal surfaces of the 3-dimensional Minkowski space, Geometry and topology of submanifolds, II (Avignon, 1988), 344-369.