Review

A Classification of Strict Walker 3-Manifold

Volume: 9 Number: 1 April 28, 2021
EN

A Classification of Strict Walker 3-Manifold

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.

Keywords

References

  1. [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. [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. [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. [4] A. S. Diallo and F. Massamba, Some properties of four-dimensional Walker manifolds, New Trends Math. Sci, 5 (2017), (3), 253-261.
  5. [5] A. S. Diallo, A. Ndiaye and A. Niang, Minimal graphs on three-dimensional Walker manifolds, To appear.
  6. [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. [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. [8] K. Nomizu and T. Sasaki, Affne Differential Geometry. Geometry of Affne Immersions. Cambridge Tracts in Mathematics Vol. 111 (Cambridge University Press, Cambridge, (1994).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Review

Authors

Athoumane Nıang This is me
Senegal

Publication Date

April 28, 2021

Submission Date

March 2, 2020

Acceptance Date

April 14, 2021

Published in Issue

Year 2021 Volume: 9 Number: 1

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.Athoumane Nıang, Ameth Ndiaye, Abdoul Salam Diallo. 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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