Araştırma Makalesi
BibTex RIS Kaynak Göster

Eight-Dimensional Walker Locally Symmetric Manifolds

Yıl 2024, Cilt: 12 Sayı: 1, 1 - 4, 30.04.2024

Öz

A pseudo-Riemannian manifold which admits a field of parallel null $r$-planes, with $r\leq \frac{m}{2}$ is a Walker $m$-manifold. The even-dimensional Walker manifolds $(m=2r)$ with fields of parallel null planes of half dimension have some special interest. The main purpose of the present paper is to study a specifc Walker metric on a $8$-dimensional manifold and to give a theorem for the metric to be locally symmetric.

Kaynakça

  • [1] R. Abounasr, A. Belhaj, J. Rasmussen and E. H. Saidi, Superstring theory on pp waves with ADE geometries, J. Phys., A 39 (2006), 2797-2841.
  • [2] M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikevic and R. Vazquez-Lorenzo. The Geometry of Walker Manifolds. Synthesis Lectures on Mathematics and Statistics, 5, (2009). (Morgan and Claypool Publishers, Williston, VT).
  • [3] M. Chaichi, E. Garcia-Rio and Y. Matsushita, Curvature properties of four-dimensional Walker metrics, Classical Quantum Gravity 22, (2005), 559-577.
  • [4] J. Davidov, J. C. Diaz-Ramos, E. Garc´ıa-R´ıo, Y. Matsushita, O. Muskarov and R. V´azquez-Lorenzo, Almost K¨ahler Walker 4-manifolds, J. Geom. Phys., 57, (2007), (3), 1075-1088.
  • [5] A. S. Diallo, S. Longwap and F. Massamba, Almost K¨ahler eight-dimensional Walker manifold, Novi Sad J. Math., 48, 2018, (1), 129-141.
  • [6] E. Garc´ıa-R´ıo E, S. Haze, N. Katayama, Y. Matsushita, Symplectic, Hermitian and K¨ahler structures on Walker 4-manifolds, J. Geom., 90 (2008), (1-2) 56-65.
  • [7] M. Iscan, A. Gezer and A. Salimov, Some properties concerning curvature tensors of eight-dimensional Walker manifolds, J. Math. Phys. Anal. Geom., 8, (2012), (1), 21-37.
  • [8] M. Iscan, Some notes concerning Norden-Walker 8-manifolds, Appl. Sci., 16, (2014), 23-31.
  • [9] S. Longwap and A. S. Diallo, Some geometric properties of a family Walker metric on an eight-dimensional manifolds, J. Nigerian Math. Soc. 41 (2022), (3), 223-234.
  • [10] Y. Matsushita, Four-dimensional Walker metrics and symplectic structure, J. Geom. Phys., 52, (2004), (1) 89-99.
  • [11] Y. Matsushita, S. Haze and P. R. Law, Almost Kahler Einstein structures on 8-dimensional Walker manifolds, Monatsh. Math., 150, (2007), 41-48.
  • [12] A. G. Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart J Math Oxford 1, (1950), (2), 69-79.
Yıl 2024, Cilt: 12 Sayı: 1, 1 - 4, 30.04.2024

Öz

Kaynakça

  • [1] R. Abounasr, A. Belhaj, J. Rasmussen and E. H. Saidi, Superstring theory on pp waves with ADE geometries, J. Phys., A 39 (2006), 2797-2841.
  • [2] M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikevic and R. Vazquez-Lorenzo. The Geometry of Walker Manifolds. Synthesis Lectures on Mathematics and Statistics, 5, (2009). (Morgan and Claypool Publishers, Williston, VT).
  • [3] M. Chaichi, E. Garcia-Rio and Y. Matsushita, Curvature properties of four-dimensional Walker metrics, Classical Quantum Gravity 22, (2005), 559-577.
  • [4] J. Davidov, J. C. Diaz-Ramos, E. Garc´ıa-R´ıo, Y. Matsushita, O. Muskarov and R. V´azquez-Lorenzo, Almost K¨ahler Walker 4-manifolds, J. Geom. Phys., 57, (2007), (3), 1075-1088.
  • [5] A. S. Diallo, S. Longwap and F. Massamba, Almost K¨ahler eight-dimensional Walker manifold, Novi Sad J. Math., 48, 2018, (1), 129-141.
  • [6] E. Garc´ıa-R´ıo E, S. Haze, N. Katayama, Y. Matsushita, Symplectic, Hermitian and K¨ahler structures on Walker 4-manifolds, J. Geom., 90 (2008), (1-2) 56-65.
  • [7] M. Iscan, A. Gezer and A. Salimov, Some properties concerning curvature tensors of eight-dimensional Walker manifolds, J. Math. Phys. Anal. Geom., 8, (2012), (1), 21-37.
  • [8] M. Iscan, Some notes concerning Norden-Walker 8-manifolds, Appl. Sci., 16, (2014), 23-31.
  • [9] S. Longwap and A. S. Diallo, Some geometric properties of a family Walker metric on an eight-dimensional manifolds, J. Nigerian Math. Soc. 41 (2022), (3), 223-234.
  • [10] Y. Matsushita, Four-dimensional Walker metrics and symplectic structure, J. Geom. Phys., 52, (2004), (1) 89-99.
  • [11] Y. Matsushita, S. Haze and P. R. Law, Almost Kahler Einstein structures on 8-dimensional Walker manifolds, Monatsh. Math., 150, (2007), 41-48.
  • [12] A. G. Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart J Math Oxford 1, (1950), (2), 69-79.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Silas Longwap

Abdoul Salam Diallo

Erken Görünüm Tarihi 29 Nisan 2024
Yayımlanma Tarihi 30 Nisan 2024
Gönderilme Tarihi 12 Eylül 2022
Kabul Tarihi 10 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Longwap, S., & Diallo, A. S. (2024). Eight-Dimensional Walker Locally Symmetric Manifolds. Konuralp Journal of Mathematics, 12(1), 1-4.
AMA Longwap S, Diallo AS. Eight-Dimensional Walker Locally Symmetric Manifolds. Konuralp J. Math. Nisan 2024;12(1):1-4.
Chicago Longwap, Silas, ve Abdoul Salam Diallo. “Eight-Dimensional Walker Locally Symmetric Manifolds”. Konuralp Journal of Mathematics 12, sy. 1 (Nisan 2024): 1-4.
EndNote Longwap S, Diallo AS (01 Nisan 2024) Eight-Dimensional Walker Locally Symmetric Manifolds. Konuralp Journal of Mathematics 12 1 1–4.
IEEE S. Longwap ve A. S. Diallo, “Eight-Dimensional Walker Locally Symmetric Manifolds”, Konuralp J. Math., c. 12, sy. 1, ss. 1–4, 2024.
ISNAD Longwap, Silas - Diallo, Abdoul Salam. “Eight-Dimensional Walker Locally Symmetric Manifolds”. Konuralp Journal of Mathematics 12/1 (Nisan 2024), 1-4.
JAMA Longwap S, Diallo AS. Eight-Dimensional Walker Locally Symmetric Manifolds. Konuralp J. Math. 2024;12:1–4.
MLA Longwap, Silas ve Abdoul Salam Diallo. “Eight-Dimensional Walker Locally Symmetric Manifolds”. Konuralp Journal of Mathematics, c. 12, sy. 1, 2024, ss. 1-4.
Vancouver Longwap S, Diallo AS. Eight-Dimensional Walker Locally Symmetric Manifolds. Konuralp J. Math. 2024;12(1):1-4.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.