Ricci solitons

In differential geometry, Ricci solitons are known as Riemannian manifolds which are solutions of the Ricci flow equation. In this thesis, some properties of Ricci soliton manifolds are examined and it is shown that the compact almost Ricci solitons with concircular potential vector field is isometric to S^n. Moreover, some characterizations of the complete m-quasi-Einstein manifold whose potential vector field concircular or concurrent to become an Einstein manifold are obtained. This work consists of six chapters. The first chapter is devoted to the introduction. In the second and third chapters, fundamental operators are summarized and some current studies are introduced. The new results that are obtained for almost Ricci solitons are given in the fourth chapter. m-quasi-Einstein manifolds which are a generalization of the Ricci solitons are introduced in the fifth chapter and also some new results on this subject are given in the last chapter.