چكيده به لاتين
In this thesis, we study the Ricci soliton structure on pseudo-Riemannian manifolds especially on closed, compact without boundary, pseudo-Riemannian manifolds. In fact, we show that unlike the Riemannian case, closed pseudo-Riemannian Ricci solitons are not necessarily gradient. Particularly, in the steady case, we have examples of closed pseudo-Riemannian Ricci solitons that unlike the Riemannian case are not necessarily Einstein manifolds. These non-trivial examples of closed pseudo- Riemannian Ricci solitons are in fact geodesically complete that admit a parallel null vector field. However, in dimension 2, we see that closed Lorentzian Ricci solitons are necessarily flat Lorentzian tori. In particular, we study some special examples of closed pseudo-Riemannian manifolds that cannot admit a Ricci soliton structure. Finally, we look at local Ricci solitons that are corresponded to static vacuum space- times.
