Ricci solitons on pseudo Riemannian generalized symmetric spaces

We study the geometry of four-dimensional pseudo Riemannian generalized symmetric spaces of type D; whose metric was explicitly described by Cerny and Kowalski. After describing their curvature properties; we classify the Killing vectors field of these spaces and more particularly, we study the existence of non-trivial (i.e., not Einstein) Ricci solitons; we show that these spaces are shrinking or expanding Ricci solitons but never steady. Moreover this Ricci soliton is not a gradient one.