Remarks on four-dimensional locally symmetric Walker manifolds

چکیده مقاله

In this paper, we examine certain geometric properties of the curvature tensor for a special case of the Walker metric, assuming g₃₃ = g₄₄ = k ≠ 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. © 2026 The Author(s).