University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 7 1 2026 05 01 Remarks on four-dimensional locally symmetric Walker manifolds 161 172 4297 10.22098/jfga.2025.18434.1186 EN Sohrab Azimpour Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran Shiva Salahvarzi Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran Journal Article 2025 09 25 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. https://jfga.uma.ac.ir/article_4297_eeee1c1e3e06acb8376ca63be4266567.pdf