Remarks on four-dimensional locally symmetric Walker manifolds

In this paper, we examine certain geometric properties of the curvature tensor for a special case of the Walker metric, assuming g۳۳ = g۴۴ = k̸ = ۰, where k is a constant, on a ۴-dimensional manifold. Finally, we investigate the necessary and sufficient conditions for the ۴-dimensional manifold with this special case of the Walker metric to be locally symmetric.

کلیدواژه ها:

Curvature tensor ، Einstein ، Locally symmetric ، Walker metric