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Year 2021, Volume: 9 Issue: 1, 148 - 153, 28.04.2021

Abstract

References

  • [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.

A Classification of Strict Walker 3-Manifold

Year 2021, Volume: 9 Issue: 1, 148 - 153, 28.04.2021

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.

References

  • [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.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Review
Authors

Athoumane Nıang This is me

Ameth Ndiaye

Abdoul Salam Diallo

Submission Date March 2, 2020
Acceptance Date April 14, 2021
Publication Date April 28, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Nıang, A., Ndiaye, A., & Diallo, A. S. (2021). A Classification of Strict Walker 3-Manifold. Konuralp Journal of Mathematics, 9(1), 148-153. https://izlik.org/JA29XT98SF
AMA 1.Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. 2021;9(1):148-153. https://izlik.org/JA29XT98SF
Chicago Nıang, Athoumane, Ameth Ndiaye, and Abdoul Salam Diallo. 2021. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics 9 (1): 148-53. https://izlik.org/JA29XT98SF.
EndNote Nıang A, Ndiaye A, Diallo AS (April 1, 2021) A Classification of Strict Walker 3-Manifold. Konuralp Journal of Mathematics 9 1 148–153.
IEEE [1]A. Nıang, A. Ndiaye, and A. S. Diallo, “A Classification of Strict Walker 3-Manifold”, Konuralp J. Math., vol. 9, no. 1, pp. 148–153, Apr. 2021, [Online]. Available: https://izlik.org/JA29XT98SF
ISNAD Nıang, Athoumane - Ndiaye, Ameth - Diallo, Abdoul Salam. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics 9/1 (April 1, 2021): 148-153. https://izlik.org/JA29XT98SF.
JAMA 1.Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. 2021;9:148–153.
MLA Nıang, Athoumane, et al. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics, vol. 9, no. 1, Apr. 2021, pp. 148-53, https://izlik.org/JA29XT98SF.
Vancouver 1.Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. [Internet]. 2021 Apr. 1;9(1):148-53. Available from: https://izlik.org/JA29XT98SF
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