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Yıl 2021, Cilt: 9 Sayı: 1, 148 - 153, 28.04.2021

Athoumane Nıang Ameth Ndiaye , Abdoul Salam Diallo

Öz

Kaynakça

  • [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

Yıl 2021, Cilt: 9 Sayı: 1, 148 - 153, 28.04.2021

Athoumane Nıang Ameth Ndiaye , Abdoul Salam Diallo

Öz

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.

Anahtar Kelimeler

Minimal surfaces Lorentz Manifold Ruled surfaces

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Athoumane Nıang

Ameth Ndiaye

Abdoul Salam Diallo

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 2 Mart 2020
Kabul Tarihi 14 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Nıang, A., Ndiaye, A., & Diallo, A. S. (2021). A Classification of Strict Walker 3-Manifold. Konuralp Journal of Mathematics, 9(1), 148-153.
AMA Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. Nisan 2021;9(1):148-153.
Chicago Nıang, Athoumane, Ameth Ndiaye, ve Abdoul Salam Diallo. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics 9, sy. 1 (Nisan 2021): 148-53.
EndNote Nıang A, Ndiaye A, Diallo AS (01 Nisan 2021) A Classification of Strict Walker 3-Manifold. Konuralp Journal of Mathematics 9 1 148–153.
IEEE A. Nıang, A. Ndiaye, ve A. S. Diallo, “A Classification of Strict Walker 3-Manifold”, Konuralp J. Math., c. 9, sy. 1, ss. 148–153, 2021.
ISNAD Nıang, Athoumane vd. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics 9/1 (Nisan 2021), 148-153.
JAMA Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. 2021;9:148–153.
MLA Nıang, Athoumane vd. “A Classification of Strict Walker 3-Manifold”. Konuralp Journal of Mathematics, c. 9, sy. 1, 2021, ss. 148-53.
Vancouver Nıang A, Ndiaye A, Diallo AS. A Classification of Strict Walker 3-Manifold. Konuralp J. Math. 2021;9(1):148-53.
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