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Azimpour, Sohrab, Salahvarzi, Shiva. (1405). Remarks on four-dimensional locally symmetric Walker manifolds. سامانه مدیریت نشریات علمی, 7(1), 161-172. doi: 10.22098/jfga.2025.18434.1186
Sohrab Azimpour; Shiva Salahvarzi. "Remarks on four-dimensional locally symmetric Walker manifolds". سامانه مدیریت نشریات علمی, 7, 1, 1405, 161-172. doi: 10.22098/jfga.2025.18434.1186
Azimpour, Sohrab, Salahvarzi, Shiva. (1405). 'Remarks on four-dimensional locally symmetric Walker manifolds', سامانه مدیریت نشریات علمی, 7(1), pp. 161-172. doi: 10.22098/jfga.2025.18434.1186
Azimpour, Sohrab, Salahvarzi, Shiva. Remarks on four-dimensional locally symmetric Walker manifolds. سامانه مدیریت نشریات علمی, 1405; 7(1): 161-172. doi: 10.22098/jfga.2025.18434.1186

Remarks on four-dimensional locally symmetric Walker manifolds

Journal of Finsler Geometry and its Applications
دوره 7، شماره 1، 2026، صفحه 161-172    اصل مقاله (267.75 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.18434.1186
نویسندگان
Sohrab Azimpour* 1؛ Shiva Salahvarzi2
1Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran
2Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran
چکیده
In this paper, we examine certain geometric properties of the curvature tensor for a special case of the Walker metric, assuming g33 = g44 = k̸ = 0, where k is a constant, on a 4-dimensional manifold. Finally, we investigate the necessary and sufficient conditions for the 4-dimensional manifold with this special case of the Walker metric to be locally symmetric.
کلیدواژه‌ها
Curvature tensor؛ Einstein؛ Locally symmetric؛ Walker metric
مراجع
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8. A. S. Diallo, and F. Massamba, Some properties of four-dimensional Walker manifolds, New Trends in Mathematical Sciences; Istanbul Vol. 5, Iss. 3, (2017), 253-261.DOI:10.20852/ntmsci.2017.200.
9. A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicate, (1978), 259-280.
10. B. Rezaei, S. Masoumi and L. Ghasemnezhad, On Quasi-Einstein Kropina Metrics, J. Finsler Geom. Appl. 6(2) (2025), 92-101.
11. A. G. Walker, Cononical form for a Ricmannian Spase with a parallel fild of Null planes, Oxford, Math. (1950), 69-79. 

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