Geodesic Mappings of Special Riemannian Manifolds

Abstract

In this paper, we will investigate the geodesic mappings of some special Riemannian manifolds. First, we will prove that if there exists an Einstein tensor preserving geodesic mapping from a quasi Einstein manifold $V_{n}$ onto a Riemannian manifold $\bar{V}_{n}$, then $\bar{V}_{n}$ is nearly quasi Einstein. Furthermore, we will obtain new results concerning the geodesic mappings of Ricci recurrent and Ricci symmetric manifolds. Next, by using these results, we will investigate the geodesic mappings of pseudo Ricci symmetric and almost pseudo Ricci symmetric manifolds.